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Series S of Discrete and Continuous Dynamical Systems only publishes theme issues. Each issue is devoted to a specific area of the mathematical, physical and engineering sciences. This area will define a research frontier that is advancing rapidly, often bridging mathematics and sciences. DCDS-S is essential reading for mathematicians, physicists, engineers and other physical scientists. The journal is published bimonthly.

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Preface: New trends on numerical analysis and analytical methods with their applications to real world problems
Abdon Atangana, Zakia Hammouch, Kolade M. Owolabi and Gisele Mephou
2019, 12(3) : ⅰ-ⅰ doi: 10.3934/dcdss.201903i +[Abstract](734) +[HTML](163) +[PDF](74.28KB)
Generalised class of Time Fractional Black Scholes equation and numerical analysis
Rodrigue Gnitchogna Batogna and Abdon Atangana
2019, 12(3) : 435-445 doi: 10.3934/dcdss.2019028 +[Abstract](1106) +[HTML](196) +[PDF](377.35KB)

It is well known now, that a Time Fractional Black Scholes Equation (TFBSE) with a time derivative of real order \begin{document}$ \alpha $\end{document} can be obtained to describe the price of an option, when for example the change in the underlying asset is assumed to follow a fractal transmission system. Fractional derivatives as they are called were introduced in option pricing in a bid to take advantage of their memory properties to capture both major jumps over small time periods and long range dependencies in markets. Recently new derivatives of Fractional Calculus with non local and/or non singular Kernel, have been introduced and have had substantial changes in modelling of some diffusion processes. Based on consistency and heuristic arguments, this work generalises previously obtained Time Fractional Black Scholes Equations to a new class of Time Fractional Black Scholes Equations. A numerical scheme solution is also derived. The stability of the numerical scheme is discussed, graphical simulations are produced to price a double barriers knock out call option.

New exact solutions for some fractional order differential equations via improved sub-equation method
Berat Karaagac
2019, 12(3) : 447-454 doi: 10.3934/dcdss.2019029 +[Abstract](952) +[HTML](171) +[PDF](846.56KB)

In this paper, improved sub-equation method is proposed to obtain new exact analytical solutions for some nonlinear fractional differential equations by means of modified Riemann Liouville derivative. The method is applied to time-fractional biological population model and space-time fractional Fisher equation successfully. Finally, simulations of new exact analytical solutions are presented graphically.

Modeling the transmission dynamics of avian influenza with saturation and psychological effect
Muhammad Altaf Khan, Muhammad Farhan, Saeed Islam and Ebenezer Bonyah
2019, 12(3) : 455-474 doi: 10.3934/dcdss.2019030 +[Abstract](1490) +[HTML](363) +[PDF](1679.39KB)

The present paper describes the mathematical analysis of an avian influenza model with saturation and psychological effect. The virus of avian influenza is not only a risk for birds but the population of human is also not safe from this. We proposed two models, one for birds and the other one for human. We consider saturated incidence rate and psychological effect in the model. The stability results for each model that is birds and human is investigated. The local and global dynamics for the disease free case of each model is proven when the basic reproduction number \begin{document}$ \mathcal{R}_{0b}<1$\end{document} and \begin{document}$ \mathcal{R}_0<1$\end{document}. Further, the local and global stability of each model is investigated in the case when \begin{document}$ \mathcal{R}_{0b}>1$\end{document} and \begin{document}$ \mathcal{R}_0>1$\end{document}. The mathematical results show that the considered saturation effect in population of birds and psychological effect in population of human does not effect the stability of equilibria, if the disease is prevalent then it can affect the number of infected humans. Numerical results are carried out in order to validate the theoretical results. Some numerical results for the proposed parameters are presented which can reduce the number of infective in the population of humans.

Numerical analysis of coupled fractional differential equations with Atangana-Baleanu fractional derivative
Ilknur Koca
2019, 12(3) : 475-486 doi: 10.3934/dcdss.2019031 +[Abstract](806) +[HTML](145) +[PDF](322.4KB)

A nonlinear system of two fractional nonlinear differential equations with Atangana-Baleanu derivative is considered in this work. General conditions under which a system solution exists and unique are presented using the fixed-point theorem method. The well-established numerical scheme is used to solve the system of equations. A numerical analysis is presented to secure the stability and convergence of the used numerical scheme.

The first integral method for two fractional non-linear biological models
Olusola Kolebaje, Ebenezer Bonyah and Lateef Mustapha
2019, 12(3) : 487-502 doi: 10.3934/dcdss.2019032 +[Abstract](865) +[HTML](217) +[PDF](2681.95KB)

Travelling wave solutions of the space and time fractional models for non-linear blood flow in large vessels and Deoxyribonucleic acid (DNA) molecule dynamics defined in the sense of Jumarie's modified Riemann-Liouville derivative via the first integral method are presented in this study. A fractional complex transformation was applied to turn the fractional biological models into an equivalent integer order ordinary differential equation. The validity of the solutions to the fractional biological models obtained with first integral method was achieved by putting them back into the models. We observed that introducing fractional order to the biological models changes the nature of the solution.

On the existence and uniqueness of the solution of an optimal control problem for Schrödinger equation
Gökçe Dİlek Küçük, Gabil Yagub and Ercan Çelİk
2019, 12(3) : 503-512 doi: 10.3934/dcdss.2019033 +[Abstract](683) +[HTML](116) +[PDF](364.62KB)

In this paper, an optimal control problem for Schrödinger equation with complex coefficient which contains gradient is examined. A theorem is given that states the existence and uniqueness of the solution of the initial-boundary value problem for Schrödinger equation. Then for the solution of the optimal control problem, two different cases are investigated. Firstly, it is shown that the optimal control problem has a unique solution for \begin{document}$α >0$\end{document} on a dense subset $G$ on the space $H$ which contains the measurable square integrable functions on \begin{document}$\left(0,l\right)$\end{document} and secondly the optimal control problem has at least one solution for any \begin{document}$α ≥ 0$\end{document} on the space $H$.

Weak Galerkin mixed finite element methods for parabolic equations with memory
Xiaomeng Li, Qiang Xu and Ailing Zhu
2019, 12(3) : 513-531 doi: 10.3934/dcdss.2019034 +[Abstract](699) +[HTML](126) +[PDF](442.02KB)

We develop a semidiscrete and a backward Euler fully discrete weak Galerkin mixed finite element method for a parabolic differential equation with memory. The optimal order error estimates in both \begin{document}$ |\|·|\| $\end{document} and \begin{document}$ L^2 $\end{document} norms are established based on a generalized elliptic projection. In the numerical experiments, the equation is solved by the weak Galerkin schemes with spaces \begin{document}$ \{[P_{k}(T)]^2, P_{k}(e), P_{k+1}(T)\} $\end{document} for \begin{document}$ k = 0 $\end{document} and the numerical convergence rates confirm the theoretical results.

A unified finite difference Chebyshev wavelet method for numerically solving time fractional Burgers' equation
Ömer Oruç, Alaattin Esen and Fatih Bulut
2019, 12(3) : 533-542 doi: 10.3934/dcdss.2019035 +[Abstract](893) +[HTML](144) +[PDF](414.65KB)

In this paper, we developed a unified method to solve time fractional Burgers' equation using the Chebyshev wavelet and L1 discretization formula. First we give the preliminary information about Chebyshev wavelet method, then we describe time discretization of the problems under consideration and then we apply Chebyshev wavelets for space discretization. The performance of the method is shown by three test problems and obtained results compared with other results available in literature.

Numerical analysis and pattern formation process for space-fractional superdiffusive systems
Kolade M. Owolabi
2019, 12(3) : 543-566 doi: 10.3934/dcdss.2019036 +[Abstract](863) +[HTML](151) +[PDF](1904.83KB)

In this paper, we consider the numerical solution of fractional-in-space reaction-diffusion equation, which is obtained from the classical reaction-diffusion equation by replacing the second-order spatial derivative with a fractional derivative of order \begin{document}$ α∈(1, 2] $\end{document}. We adopt a class of second-order approximations, based on the weighted and shifted Grünwald difference operators in Riemann-Liouville sense to numerically simulate two multicomponent systems with fractional-order in higher dimensions. The efficiency and accuracy of the numerical schemes are justified by reporting the norm infinity and norm relative errors as well as their convergence. The complexity of the dynamics in the equation is theoretically discussed by conducting its local and global stability analysis and Numerical experiments are performed to back-up the theoretical claims.

High-order solvers for space-fractional differential equations with Riesz derivative
Kolade M. Owolabi and Abdon Atangana
2019, 12(3) : 567-590 doi: 10.3934/dcdss.2019037 +[Abstract](912) +[HTML](145) +[PDF](2009.11KB)

This paper proposes the computational approach for fractional-in-space reaction-diffusion equation, which is obtained by replacing the space second-order derivative in classical reaction-diffusion equation with the Riesz fractional derivative of order \begin{document}$ α $\end{document} in \begin{document}$ (0, 2] $\end{document}. The proposed numerical scheme for space fractional reaction-diffusion equations is based on the finite difference and Fourier spectral approximation methods. The paper utilizes a range of higher-order time stepping solvers which exhibit third-order accuracy in the time domain and spectral accuracy in the spatial domain to solve some fractional-in-space reaction-diffusion equations. The numerical experiment shows that the third-order ETD3RK scheme outshines its third-order counterparts, taking into account the computational time and accuracy. Applicability of the proposed methods is further tested with a higher dimensional system. Numerical simulation results show that pattern formation process in the classical sense is the same as in fractional scenarios.

Efficient numerical method for a model arising in biological stoichiometry of tumour dynamics
Kolade M. Owolabi, Kailash C. Patidar and Albert Shikongo
2019, 12(3) : 591-613 doi: 10.3934/dcdss.2019038 +[Abstract](942) +[HTML](234) +[PDF](536.33KB)

In this paper, we extend a system of coupled first order non-linear system of delay differential equations (DDEs) arising in modeling of stoichiometry of tumour dynamics, to a system of diffusion-reaction system of partial delay differential equations (PDDEs). Since tumor cells are further modified by blood supply through the vascularization process, we determine the local uniform steady states of the homogeneous tumour growth model with respect to the vascularization process. We show that the steady states are globally stable, determine the existence of Hopf bifurcation of the homogeneous tumour growth model with respect to the vascularization process. We derive, analyse and implement a fitted operator finite difference method (FOFDM) to solve the extended model. This FOFDM is analyzed for convergence and we observe seen that it has second-order accuracy. Some numerical results confirming theoretical observations are also presented. These results are comparable with those obtained in the literature.

The discrete homotopy perturbation Sumudu transform method for solving partial difference equations
Figen Özpinar and Fethi Bin Muhammad Belgacem
2019, 12(3) : 615-624 doi: 10.3934/dcdss.2019039 +[Abstract](634) +[HTML](109) +[PDF](6929.15KB)

In this paper, we introduce a combined form of the discrete Sumudu transform method with the discrete homotopy perturbation method to solve linear and nonlinear partial difference equations. This method is called the discrete homotopy perturbation Sumudu transform method(DHPSTM). The results reveal that the introduced method is very efficient, simple and can be applied to other linear and nonlinear difference equations. The nonlinear terms can be easily handled by use of He's polynomials.

Barycentric spectral domain decomposition methods for valuing a class of infinite activity Lévy models
Edson Pindza, Francis Youbi, Eben Maré and Matt Davison
2019, 12(3) : 625-643 doi: 10.3934/dcdss.2019040 +[Abstract](864) +[HTML](106) +[PDF](636.33KB)

A new barycentric spectral domain decomposition methods algorithm for solving partial integro-differential models is described. The method is applied to European and butterfly call option pricing problems under a class of infinite activity Lévy models. It is based on the barycentric spectral domain decomposition methods which allows the implementation of the boundary conditions in an efficient way. After the approximation of the spatial derivatives, we obtained the semi-discrete equations. The computation of these equations is performed by using the barycentric spectral domain decomposition method. This is achieved with the implementation of an exponential time integration scheme. Several numerical tests for the pricing of European and butterfly options are given to illustrate the efficiency and accuracy of this new algorithm. We also show that Greek options, such as Delta and Gamma sensitivity, are computed with no spurious oscillation.

Couette flows of a viscous fluid with slip effects and non-integer order derivative without singular kernel
Muhammad Bilal Riaz, Naseer Ahmad Asif, Abdon Atangana and Muhammad Imran Asjad
2019, 12(3) : 645-664 doi: 10.3934/dcdss.2019041 +[Abstract](740) +[HTML](121) +[PDF](821.22KB)

Couette flows of an incompressible viscous fluid with non-integer order derivative without singular kernel produced by the motion of a flat plate are analyzed under the slip condition at boundaries. An analytical transform approach is used to obtain the exact expressions for velocity and shear stress. Three particular cases from the general results with and without slip at the wall are obtained. These solutions, which are organized in simple forms in terms of exponential and trigonometric functions, can be conveniently engaged to obtain known solutions from the literature. The control of the new non-integer order derivative on the velocity of the fluid moreover a comparative study with an older model, is analyzed for some flows with practical applications. The non-integer order derivative with non-singular kernel is more appropriate for handling mathematical calculations of obtained solutions.

Comparative study of a cubic autocatalytic reaction via different analysis methods
Khaled Mohammed Saad and Eman Hussain Faissal AL-Sharif
2019, 12(3) : 665-684 doi: 10.3934/dcdss.2019042 +[Abstract](947) +[HTML](123) +[PDF](2057.25KB)

In this paper we discuss an approximate solutions of the space-time fractional cubic autocatalytic chemical system (STFCACS) equations. The main objective is to find and compare approximate solutions of these equations found using Optimal q-Homotopy Analysis Method (Oq-HAM), Homotopy Analysis Transform Method (HATM), Varitional Iteration Method (VIM) and Adomian Decomposition Method (ADM).

Spectral Jacobi-Galerkin methods and iterated methods for Fredholm integral equations of the second kind with weakly singular kernel
Yin Yang and Yunqing Huang
2019, 12(3) : 685-702 doi: 10.3934/dcdss.2019043 +[Abstract](636) +[HTML](112) +[PDF](489.43KB)

We consider spectral and pseudo-spectral Jacobi-Galerkin methods and corresponding iterated methods for Fredholm integral equations of the second kind with weakly singular kernel. The Gauss-Jacobi quadrature formula is used to approximate the integral operator and the inner product based on the Jacobi weight is implemented in the weak formulation in the numerical implementation. We obtain the convergence rates for the approximated solution and iterated solution in weakly singular Fredholm integral equations, which show that the errors of the approximate solution decay exponentially in \begin{document}$L^∞$\end{document}-norm and weighted \begin{document}$L^2$\end{document}-norm. The numerical examples are given to illustrate the theoretical results.

Libration points in the restricted three-body problem: Euler angles, existence and stability
Hadia H. Selim, Juan L. G. Guirao and Elbaz I. Abouelmagd
2018doi: 10.3934/dcdss.2019044 +[Abstract](351) +[HTML](237) +[PDF](297.45KB)
Tight independent set neighborhood union condition for fractional critical deleted graphs and ID deleted graphs
Wei Gao, Darko Dimitrov and Hosam Abdo
2018doi: 10.3934/dcdss.2019045 +[Abstract](340) +[HTML](248) +[PDF](343.47KB)
A real attractor non admitting a connected feasible open set
Manuel Fernández-Martínez
2018doi: 10.3934/dcdss.2019046 +[Abstract](327) +[HTML](179) +[PDF](245.18KB)
Design of one type of linear network prediction controller for multi-agent system
Hong Man, Yibin Yu, Yuebang He and Hui Huang
2018doi: 10.3934/dcdss.2019047 +[Abstract](300) +[HTML](227) +[PDF](323.32KB)
A SIR-based model for contact-based messaging applications supported by permanent infrastructure
J. Alberto Conejero, Enrique Hernández-Orallo, Pietro Manzoni and Marina Murillo-Arcila
2018doi: 10.3934/dcdss.2019048 +[Abstract](310) +[HTML](205) +[PDF](673.04KB)
Risk assessment for enterprise merger and acquisition via multiple classifier fusion
Yinying Duan, Yong Ye and Zhichao Liu
2018doi: 10.3934/dcdss.2019049 +[Abstract](310) +[HTML](290) +[PDF](6101.98KB)
Nonlinear dynamics tools for solving problems coming from engineering, physics, chemistry, ecology and medicine
Wei Gao and Juan L. G. Guirao
2018doi: 10.3934/dcdss.201904i +[Abstract](428) +[HTML](206) +[PDF](130.89KB)
A new approach for worst-case regret portfolio optimization problem
Ying Ji, Shaojian Qu and Yeming Dai
2018doi: 10.3934/dcdss.2019050 +[Abstract](281) +[HTML](242) +[PDF](339.6KB)
Tourism destination competitiveness evaluation in Sichuan province using TOPSIS model based on information entropy weights
Tao Gu, Peiyu Ren, Maozhu Jin and Hua Wang
2018doi: 10.3934/dcdss.2019051 +[Abstract](310) +[HTML](212) +[PDF](354.06KB)
On the design of full duplex wireless system with chaotic sequences
Ruwu Xiao, Geng Li and Yuping Zhao
2018doi: 10.3934/dcdss.2019052 +[Abstract](277) +[HTML](235) +[PDF](1118.73KB)
Total factor productivity growth and technological change in the telecommunications industry
Xuchen Lin, Ting-Jie Lu and Xia Chen
2018doi: 10.3934/dcdss.2019053 +[Abstract](357) +[HTML](221) +[PDF](390.08KB)
Collaborative filtering recommendation algorithm towards intelligent community
Wei Fu, Jun Liu and Yirong Lai
2018doi: 10.3934/dcdss.2019054 +[Abstract](350) +[HTML](220) +[PDF](406.65KB)
Uyghur morphological analysis using joint conditional random fields: Based on small scaled corpus
Ghalip Abdukerim, Eziz Tursun, Yating Yang and Xiao Li
2018doi: 10.3934/dcdss.2019055 +[Abstract](381) +[HTML](286) +[PDF](252.96KB)
A mathematical analysis for the forecast research on tourism carrying capacity to promote the effective and sustainable development of tourism
Yanan Wang, Tao Xie and Xiaowen Jie
2018doi: 10.3934/dcdss.2019056 +[Abstract](289) +[HTML](248) +[PDF](436.95KB)
The perturbed photogravitational restricted three-body problem: Analysis of resonant periodic orbits
Niraj Pathak, V. O. Thomas and Elbaz I. Abouelmagd
2018doi: 10.3934/dcdss.2019057 +[Abstract](353) +[HTML](294) +[PDF](4314.84KB)
An independent set degree condition for fractional critical deleted graphs
Wei Gao, Juan Luis García Guirao, Mahmoud Abdel-Aty and Wenfei Xi
2018doi: 10.3934/dcdss.2019058 +[Abstract](335) +[HTML](235) +[PDF](344.92KB)
Wireless sensor network energy efficient coverage method based on intelligent optimization algorithm
Yang Chen, Xiaoguang Xu and Yong Wang
2018doi: 10.3934/dcdss.2019059 +[Abstract](301) +[HTML](248) +[PDF](2852.11KB)
An efficient face recognition algorithm using the improved convolutional neural network
Honggang Yu
2018doi: 10.3934/dcdss.2019060 +[Abstract](324) +[HTML](241) +[PDF](3133.85KB)
Stock price fluctuation prediction method based on time series analysis
Xiao-Qian Jiang and Lun-Chuan Zhang
2018doi: 10.3934/dcdss.2019061 +[Abstract](325) +[HTML](438) +[PDF](1945.97KB)
A nonlinear empirical analysis on influence factor of circulation efficiency
Wu Chanti and Qiu Youzhen
2018doi: 10.3934/dcdss.2019062 +[Abstract](292) +[HTML](204) +[PDF](352.12KB)
Atmospheric environmental quality assessment method based on analytic hierarchy process
Wendai Lv and Siping Ji
2018doi: 10.3934/dcdss.2019063 +[Abstract](335) +[HTML](227) +[PDF](3095.26KB)
Applications of mathematics to maritime search
Jinling Wei, Jinming Zhang, Meishuang Dong, Fan Zhang, Yunmo Chen, Sha Jin and Zhike Han
2018doi: 10.3934/dcdss.2019064 +[Abstract](348) +[HTML](218) +[PDF](538.49KB)
A pricing option approach based on backward stochastic differential equation theory
Xiao-Qian Jiang and Lun-Chuan Zhang
2018doi: 10.3934/dcdss.2019065 +[Abstract](368) +[HTML](193) +[PDF](544.92KB)
A solution of TSP based on the ant colony algorithm improved by particle swarm optimization
Miao Yu
2018doi: 10.3934/dcdss.2019066 +[Abstract](330) +[HTML](229) +[PDF](707.63KB)
Environmental game modeling with uncertainties
Ying Ji, Shaojian Qu and Fuxing Chen
2018doi: 10.3934/dcdss.2019067 +[Abstract](328) +[HTML](208) +[PDF](409.22KB)
Uniform $L^1$ stability of the inelastic Boltzmann equation with large external force for hard potentials
Shaofei Wu, Mingqing Wang, Maozhu Jin, Yuntao Zou and Lijun Song
2018doi: 10.3934/dcdss.2019068 +[Abstract](310) +[HTML](224) +[PDF](376.5KB)
Enterprise inefficient investment behavior analysis based on regression analysis
Wei Li and Yun Teng
2018doi: 10.3934/dcdss.2019069 +[Abstract](297) +[HTML](185) +[PDF](367.84KB)
Laurence Cherfils, Alain Cimetière, Aziz Hamdouni, Michel Jean and Elaine Pratt
2018doi: 10.3934/dcdss.201906i +[Abstract](297) +[HTML](178) +[PDF](81.11KB)
Error minimization with global optimization for difference of convex functions
Zhongliang Deng and Enwen Hu
2018doi: 10.3934/dcdss.2019070 +[Abstract](332) +[HTML](194) +[PDF](858.89KB)
A novel road dynamic simulation approach for vehicle driveline experiments
Wen-Li Li, Jing-Jing Wang, Xiang-Kui Zhang and Peng Yi
2018doi: 10.3934/dcdss.2019071 +[Abstract](272) +[HTML](235) +[PDF](33081.19KB)
Major project risk assessment method based on BP neural network
Lidong Liu, Fajie Wei and Shenghan Zhou
2018doi: 10.3934/dcdss.2019072 +[Abstract](375) +[HTML](270) +[PDF](28388.61KB)
A new face feature point matrix based on geometric features and illumination models for facial attraction analysis
Jian Zhao, Fang Deng, Jian Jia, Chunmeng Wu, Haibo Li, Yuan Shi and Shunli Zhang
2018doi: 10.3934/dcdss.2019073 +[Abstract](309) +[HTML](216) +[PDF](1584.87KB)
A dynamical system study for the ecological development of mineral resources in minority areas
Yuyan Luo, Yong Qin, Zhong Wang and Jun Wang
2018doi: 10.3934/dcdss.2019074 +[Abstract](311) +[HTML](220) +[PDF](468.9KB)
Estimation of normal distribution parameters and its application to carbonation depth of concrete girder bridges
Yuan Li, Lei Yan, Lingbo Wang and Wei Hou
2018doi: 10.3934/dcdss.2019075 +[Abstract](249) +[HTML](209) +[PDF](293.69KB)
An AIMMS-based decision-making model for optimizing the intelligent stowage of export containers in a single bay
Jian Jin and Weijian Mi
2018doi: 10.3934/dcdss.2019076 +[Abstract](351) +[HTML](221) +[PDF](1335.88KB)
Research on regional clustering and two-stage SVM method for container truck recognition
Chao Mi, Jun Wang, Weijian Mi, Youfang Huang, Zhiwei Zhang, Yongsheng Yang, Jun Jiang and Postolache Octavian
2018doi: 10.3934/dcdss.2019077 +[Abstract](335) +[HTML](243) +[PDF](3483.25KB)
Efficient systolic multiplications in composite fields for cryptographic systems
Haibo Yi
2018doi: 10.3934/dcdss.2019078 +[Abstract](291) +[HTML](191) +[PDF](356.69KB)
The heterogeneous fleet location routing problem with simultaneous pickup and delivery and overloads
Xuefeng Wang
2018doi: 10.3934/dcdss.2019079 +[Abstract](356) +[HTML](235) +[PDF](465.91KB)
Three-dimensional computer simulation of twill woven fabric by using polynomial mathematical model
Fang Qin, Ying Jiang and Ping Gu
2018doi: 10.3934/dcdss.2019080 +[Abstract](301) +[HTML](194) +[PDF](877.68KB)
Vulnerability of super connected split graphs and bisplit graphs
Litao Guo and Bernard L. S. Lin
2018doi: 10.3934/dcdss.2019081 +[Abstract](279) +[HTML](198) +[PDF](160.2KB)
Cores and optimal fuzzy communication structures of fuzzy games
Jiaquan Zhan and Fanyong Meng
2018doi: 10.3934/dcdss.2019082 +[Abstract](381) +[HTML](225) +[PDF](384.57KB)
Research on iterative repair algorithm of Hyperchaotic image based on support vector machine
Xin Li, Ziguan Cui, Linhui Sun, Guanming Lu and Debnath Narayan
2018doi: 10.3934/dcdss.2019083 +[Abstract](400) +[HTML](221) +[PDF](1131.09KB)
Reversible hidden data access algorithm in cloud computing environment
Jinsong Xu
2018doi: 10.3934/dcdss.2019084 +[Abstract](362) +[HTML](238) +[PDF](1019.79KB)
Analysis of the clustering fusion algorithm for multi-band color image
Jiangchuan Fan, Xinyu Guo, Jianjun Du, Weiliang Wen, Xianju Lu and Brahmani Louiza
2018doi: 10.3934/dcdss.2019085 +[Abstract](331) +[HTML](210) +[PDF](1423.76KB)
Automatic tracking and positioning algorithm for moving targets in complex environment
Rong Liu and Saini Jonathan Tishari
2018doi: 10.3934/dcdss.2019086 +[Abstract](277) +[HTML](201) +[PDF](1004.57KB)
A new text information extraction algorithm of video image under multimedia environment
Xiaohong Zhu, Lihe Zhou, Zili Yang and Joyati Debnath
2018doi: 10.3934/dcdss.2019087 +[Abstract](300) +[HTML](199) +[PDF](1712.04KB)
Research on the matching algorithm for heterologous image after deformation in the same scene
Xiaohong Zhu, Zili Yang and Tabharit Zoubir
2018doi: 10.3934/dcdss.2019088 +[Abstract](294) +[HTML](177) +[PDF](1462.14KB)
X-ray image global enhancement algorithm in medical image classification
Wenzhong Zhu, Huanlong Jiang, Erli Wang, Yani Hou, Lidong Xian and Joyati Debnath
2018doi: 10.3934/dcdss.2019089 +[Abstract](331) +[HTML](270) +[PDF](719.92KB)
Special issue on fractal geometry, dynamical systems, and their applications
Michael Barnsley, James Keesling and Mrinal Kanti Roychowdhury
2019doi: 10.3934/dcdss.201908i +[Abstract](304) +[HTML](115) +[PDF](108.2KB)
Efficient extraction algorithm for local fuzzy features of dynamic images
Yunsai Chen, Zhao Yang, Liang Ma, Peng Li, Yongjie Pang, Xin Zhao and Wenyi Yang
2018doi: 10.3934/dcdss.2019090 +[Abstract](364) +[HTML](199) +[PDF](1929.18KB)
A high precision data encryption algorithm in wireless network mobile communication
Aiwan Fan, Qiming Wang and Joyati Debnath
2018doi: 10.3934/dcdss.2019091 +[Abstract](291) +[HTML](250) +[PDF](1221.55KB)
Optimization algorithm for embedded Linux remote video monitoring system oriented to the internet of things (IOT)
Wenbo Fu and Debnath Narayan
2018doi: 10.3934/dcdss.2019092 +[Abstract](322) +[HTML](232) +[PDF](2305.53KB)
Optical chaotic secure algorithm based on space laser communication
Ruiqiang Guo and Lu Song
2018doi: 10.3934/dcdss.2019093 +[Abstract](360) +[HTML](227) +[PDF](686.93KB)
An optimization detection algorithm for complex intrusion interference signal in mobile wireless network
Li Gang
2018doi: 10.3934/dcdss.2019094 +[Abstract](320) +[HTML](193) +[PDF](966.29KB)
Intelligent recognition algorithm for social network sensitive information based on classification technology
Weiping Li, Haiyan Wu and Jie Yang
2018doi: 10.3934/dcdss.2019095 +[Abstract](318) +[HTML](197) +[PDF](378.69KB)
The optimization algorithm for blind processing of high frequency signal of capacitive sensor
Yuanjia Ma
2018doi: 10.3934/dcdss.2019096 +[Abstract](285) +[HTML](253) +[PDF](596.85KB)
Multi-objective optimization algorithm based on improved particle swarm in cloud computing environment
Min Zhang and Gang Li
2018doi: 10.3934/dcdss.2019097 +[Abstract](404) +[HTML](234) +[PDF](415.47KB)
Research on image digital watermarking optimization algorithm under virtual reality technology
Yi Zhang and Xiao-Li Ma
2018doi: 10.3934/dcdss.2019098 +[Abstract](343) +[HTML](193) +[PDF](468.83KB)
An algorithm for reversible information hiding of encrypted medical images in homomorphic encrypted domain
Xueyan Wu
2018doi: 10.3934/dcdss.2019099 +[Abstract](362) +[HTML](213) +[PDF](495.83KB)
Data encryption algorithm for e-commerce platform based on blockchain technology
Fei Gao
2018doi: 10.3934/dcdss.2019100 +[Abstract](473) +[HTML](351) +[PDF](438.71KB)
EMD and GNN-AdaBoost fault diagnosis for urban rail train rolling bearings
Guoqiang Cai, Chen Yang, Yue Pan and Jiaojiao Lv
2018doi: 10.3934/dcdss.2019101 +[Abstract](296) +[HTML](207) +[PDF](3424.44KB)
An efficient RFID anonymous batch authentication protocol based on group signature
Jie Xu and Lanjun Dang
2018doi: 10.3934/dcdss.2019102 +[Abstract](355) +[HTML](214) +[PDF](427.27KB)
Multi-machine and multi-task emergency allocation algorithm based on precedence rules
Fan Zhang, Guifa Teng, Mengmeng Gao, Shuai Zhang and Jingjing Zhang
2018doi: 10.3934/dcdss.2019103 +[Abstract](308) +[HTML](196) +[PDF](443.3KB)
Double layer programming model to the scheduling of remote sensing data processing tasks
Min-Fan He, Li-Ning Xing, Wen Li, Shang Xiang and Xu Tan
2018doi: 10.3934/dcdss.2019104 +[Abstract](362) +[HTML](198) +[PDF](3192.23KB)
A novel approach to improve the accuracy of the box dimension calculations: Applications to trabecular bone quality
M. Fernández-Martínez, Yolanda Guerrero-Sánchez and Pía López-Jornet
2018doi: 10.3934/dcdss.2019105 +[Abstract](272) +[HTML](181) +[PDF](16275.71KB)
Existence theorem for a first-order Koiter nonlinear shell model
Sylvia Anicic
2018doi: 10.3934/dcdss.2019106 +[Abstract](284) +[HTML](183) +[PDF](321.52KB)
Formal asymptotic analysis of elastic beams and thin-walled beams: A derivation of the Vlassov equations and their generalization to the anisotropic heterogeneous case
Patrick Ballard and Bernadette Miara
2018doi: 10.3934/dcdss.2019107 +[Abstract](328) +[HTML](183) +[PDF](519.08KB)
Magnetic forces in and on a magnet
Alain Bossavit
2018doi: 10.3934/dcdss.2019108 +[Abstract](240) +[HTML](208) +[PDF](333.8KB)
Analysis of discretized parabolic problems modeling electrostatic micro-electromechanical systems
Laurence Cherfils, Alain Miranville, Shuiran Peng and Chuanju Xu
2018doi: 10.3934/dcdss.2019109 +[Abstract](322) +[HTML](216) +[PDF](884.5KB)
Complex ray in anisotropic solids: Extended Fermat's principle
Marc Deschamps and Olivier Poncelet
2018doi: 10.3934/dcdss.2019110 +[Abstract](252) +[HTML](197) +[PDF](795.84KB)
On the controllability of racing sailing boats with foils
Philippe Destuynder and Caroline Fabre
2018doi: 10.3934/dcdss.2019111 +[Abstract](262) +[HTML](194) +[PDF](10229.27KB)
Direct construction of symmetry-breaking directions in bifurcation problems with spherical symmetry
Sanjay Dharmavaram and Timothy J. Healey
2018doi: 10.3934/dcdss.2019112 +[Abstract](394) +[HTML](192) +[PDF](6179.96KB)
Efficient high-order implicit solvers for the dynamic of thin-walled beams with open cross section under external arbitrary loadings
Ahmed El Kaimbillah, Oussama Bourihane, Bouazza Braikat, Mohammad Jamal, Foudil Mohri and Noureddine Damil
2018doi: 10.3934/dcdss.2019113 +[Abstract](391) +[HTML](422) +[PDF](3536.02KB)
Approximation of semi-groups in the sense of Trotter and asymptotic mathematical modeling in physics of continuous media
Christian Licht and Thibaut Weller
2018doi: 10.3934/dcdss.2019114 +[Abstract](343) +[HTML](224) +[PDF](544.42KB)
POD basis interpolation via Inverse Distance Weighting on Grassmann manifolds
Rolando Mosquera, Aziz Hamdouni, Abdallah El Hamidi and Cyrille Allery
2018doi: 10.3934/dcdss.2019115 +[Abstract](416) +[HTML](214) +[PDF](1027.49KB)
Dynamics of locally linearizable complex two dimensional cubic Hamiltonian systems
Yangyou Pan, Yuzhen Bai and Xiang Zhang
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Topological remarks and new examples of persistence of diversity in biological dynamics
Evariste Sanchez-Palencia and Jean-Pierre Françoise
2018doi: 10.3934/dcdss.2019117 +[Abstract](331) +[HTML](198) +[PDF](745.0KB)
Multi-point Taylor series to solve differential equations
Djédjé Sylvain Zézé, Michel Potier-Ferry and Yannick Tampango
2018doi: 10.3934/dcdss.2019118 +[Abstract](419) +[HTML](207) +[PDF](455.71KB)
The work of Norman Dancer
Yihong Du
2018doi: 10.3934/dcdss.2019119 +[Abstract](226) +[HTML](130) +[PDF](563.04KB)
On a degree associated with the Gross-Pitaevskii system with a large parameter
E. Norman Dancer
2018doi: 10.3934/dcdss.2019120 +[Abstract](190) +[HTML](93) +[PDF](252.8KB)
Subharmonic solutions for a class of Lagrangian systems
Anouar Bahrouni, Marek Izydorek and Joanna Janczewska
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On good deformations of $ A_m $-singularities
Zalman Balanov and Yakov Krasnov
2018doi: 10.3934/dcdss.2019122 +[Abstract](203) +[HTML](113) +[PDF](422.7KB)
The Morse property for functions of Kirchhoff-Routh path type
Thomas Bartsch, Anna Maria Micheletti and Angela Pistoia
2018doi: 10.3934/dcdss.2019123 +[Abstract](199) +[HTML](105) +[PDF](433.5KB)
Dihedral molecular configurations interacting by Lennard-Jones and Coulomb forces
Irina Berezovik, Wieslaw Krawcewicz and Qingwen Hu
2018doi: 10.3934/dcdss.2019124 +[Abstract](178) +[HTML](96) +[PDF](300.33KB)
Global bifurcations and a priori bounds of positive solutions for coupled nonlinear Schrödinger Systems
Guowei Dai, Rushun Tian and Zhitao Zhang
2018doi: 10.3934/dcdss.2019125 +[Abstract](194) +[HTML](131) +[PDF](530.21KB)
Least energy solutions for fractional Kirchhoff type equations involving critical growth
Yinbin Deng and Wentao Huang
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Branching and bifurcation
Patrick M. Fitzpatrick and Jacobo Pejsachowicz
2018doi: 10.3934/dcdss.2019127 +[Abstract](212) +[HTML](98) +[PDF](459.95KB)
Multiple solutions for a critical quasilinear equation with Hardy potential
Fengshuang Gao and Yuxia Guo
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Global symmetry-breaking bifurcations of critical orbits of invariant functionals
Anna Goƚȩbiewska, Norimichi Hirano and Sƚawomir Rybicki
2018doi: 10.3934/dcdss.2019129 +[Abstract](190) +[HTML](98) +[PDF](430.91KB)
Selective Pyragas control of Hamiltonian systems
Edward Hooton, Pavel Kravetc, Dmitrii Rachinskii and Qingwen Hu
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Existence of positive ground state solutions for Choquard equation with variable exponent growth
Gui-Dong Li and Chun-Lei Tang
2018doi: 10.3934/dcdss.2019131 +[Abstract](246) +[HTML](101) +[PDF](481.63KB)
Solutions of nonlinear periodic Dirac equations with periodic potentials
Xiaoyan Lin and Xianhua Tang
2018doi: 10.3934/dcdss.2019132 +[Abstract](214) +[HTML](93) +[PDF](403.85KB)
A Leslie-Gower predator-prey model with a free boundary
Yunfeng Liu, Zhiming Guo, Mohammad El Smaily and Lin Wang
2018doi: 10.3934/dcdss.2019133 +[Abstract](198) +[HTML](108) +[PDF](460.06KB)
Periodic and subharmonic solutions for a 2$n$th-order $\phi_c$-Laplacian difference equation containing both advances and retardations
Peng Mei, Zhan Zhou and Genghong Lin
2018doi: 10.3934/dcdss.2019134 +[Abstract](201) +[HTML](101) +[PDF](381.32KB)
Traveling waves in Fermi-Pasta-Ulam chains with nonlocal interaction
Alexander Pankov
2018doi: 10.3934/dcdss.2019135 +[Abstract](214) +[HTML](129) +[PDF](406.92KB)
Ground states of nonlinear Schrödinger equations with fractional Laplacians
Zupei Shen, Zhiqing Han and Qinqin Zhang
2018doi: 10.3934/dcdss.2019136 +[Abstract](228) +[HTML](111) +[PDF](387.3KB)
On periodic solutions in the Whitney's inverted pendulum problem
Roman Srzednicki
2018doi: 10.3934/dcdss.2019137 +[Abstract](210) +[HTML](92) +[PDF](381.34KB)
Positive solutions of doubly coupled multicomponent nonlinear Schrödinger systems
Jiabao Su, Rushun Tian and Zhi-Qiang Wang
2018doi: 10.3934/dcdss.2019138 +[Abstract](206) +[HTML](101) +[PDF](507.51KB)
Ground state homoclinic solutions for a second-order Hamiltonian system
Xiaoping Wang
2018doi: 10.3934/dcdss.2019139 +[Abstract](226) +[HTML](101) +[PDF](447.37KB)
The mean and noise of FPT modulated by promoter architecture in gene networks
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2018doi: 10.3934/dcdss.2019140 +[Abstract](219) +[HTML](107) +[PDF](475.08KB)
Bifurcation analysis of a stage-structured predator-prey model with prey refuge
Qing Zhu, Huaqin Peng, Xiaoxiao Zheng and Huafeng Xiao
2018doi: 10.3934/dcdss.2019141 +[Abstract](211) +[HTML](96) +[PDF](367.13KB)
Shadowing is generic on dendrites
Will Brian, Jonathan Meddaugh and Brian Raines
2019doi: 10.3934/dcdss.2019142 +[Abstract](181) +[HTML](98) +[PDF](333.27KB)
Free probability on $ C^{*}$-algebras induced by hecke algebras over primes
Ilwoo Cho and Palle Jorgense
2019doi: 10.3934/dcdss.2019143 +[Abstract](170) +[HTML](88) +[PDF](556.98KB)
Orbit portraits in non-autonomous iteration
Mark Comerford and Todd Woodard
2019doi: 10.3934/dcdss.2019144 +[Abstract](150) +[HTML](91) +[PDF](3443.77KB)
Solving the Babylonian problem of quasiperiodic rotation rates
Suddhasattwa Das, Yoshitaka Saiki, Evelyn Sander and James A. Yorke
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Dynamical properties of endomorphisms, multiresolutions, similarity and orthogonality relations
Palle Jorgensen and Feng Tian
2019doi: 10.3934/dcdss.2019146 +[Abstract](192) +[HTML](101) +[PDF](1021.99KB)
Informing the structure of complex Hadamard matrix spaces using a flow
Francis C. Motta and Patrick D. Shipman
2019doi: 10.3934/dcdss.2019147 +[Abstract](141) +[HTML](92) +[PDF](2129.44KB)
On a semigroup problem
Viorel Nitica and Andrei Török
2019doi: 10.3934/dcdss.2019148 +[Abstract](194) +[HTML](95) +[PDF](400.77KB)
Stable sets of planar homeomorphisms with translation pseudo-arcs
Francisco R. Ruiz del Portal
2019doi: 10.3934/dcdss.2019149 +[Abstract](170) +[HTML](87) +[PDF](469.23KB)
Hereditarily non uniformly perfect sets
Rich Stankewitz, Toshiyuki Sugawa and Hiroki Sumi
2019doi: 10.3934/dcdss.2019150 +[Abstract](162) +[HTML](86) +[PDF](408.13KB)
Thurston's algorithm and rational maps from quadratic polynomial matings
Mary Wilkerson
2019doi: 10.3934/dcdss.2019151 +[Abstract](226) +[HTML](94) +[PDF](4291.42KB)
Preface: Special issue of DCDS-S dedicated to the 70th birthday of Norman Dancer
Zalman Balanov, Wiesław Krawcewicz and Jianshe Yu
2018doi: 10.3934/dcdss.20197i +[Abstract](239) +[HTML](101) +[PDF](1369.58KB)
A cyclic system with delay and its characteristic equation
Elena Braverman, Karel Hasik, Anatoli F. Ivanov and Sergei I. Trofimchuk
2019doi: 10.3934/dcdss.2020001 +[Abstract](140) +[HTML](76) +[PDF](978.84KB)
Long-time behavior of positive solutions of a differential equation with state-dependent delay
Josef Diblík
2019doi: 10.3934/dcdss.2020002 +[Abstract](132) +[HTML](91) +[PDF](424.57KB)
A periodic solution with non-simple oscillation for an equation with state-dependent delay and strictly monotonic negative feedback
Benjamin B. Kennedy
2019doi: 10.3934/dcdss.2020003 +[Abstract](119) +[HTML](75) +[PDF](2370.68KB)
Existence of strictly decreasing positive solutions of linear differential equations of neutral type
Josef Diblík and Zdeněk Svoboda
2019doi: 10.3934/dcdss.2020004 +[Abstract](134) +[HTML](81) +[PDF](445.59KB)
Generalised Lyapunov-Razumikhin techniques for scalar state-dependent delay differential equations
F. M. G. Magpantay and A. R. Humphries
2019doi: 10.3934/dcdss.2020005 +[Abstract](30) +[HTML](10) +[PDF](10539.13KB)
Stabilization in a chemotaxis model for virus infection
Nicola Bellomo and Youshan Tao
2019doi: 10.3934/dcdss.2020006 +[Abstract](149) +[HTML](70) +[PDF](424.81KB)
Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity
Tobias Black
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Boundedness and homogeneous asymptotics for a fractional logistic Keller-Segel equations
Jan Burczak and Rafael Granero-Belinchón
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Global existence in the 1D quasilinear parabolic-elliptic chemotaxis system with critical nonlinearity
Tomasz Cieślak and Kentarou Fujie
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On a chemotaxis model with competitive terms arising in angiogenesis
Manuel Delgado, Inmaculada Gayte, Cristian Morales-Rodrigo and Antonio Suárez
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Global asymptotic stability in a chemotaxis-growth model for tumor invasion
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Boundedness in a quasilinear fully parabolic Keller-Segel system via maximal Sobolev regularity
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Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system
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Decay in chemotaxis systems with a logistic term
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Improvement of conditions for asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity
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Existence of traveling wave solutions to parabolic-elliptic-elliptic chemotaxis systems with logistic source
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Global solvability in a two-dimensional self-consistent chemotaxis-Navier-Stokes system
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Preface: Delay differential equations with state-dependent delays and their applications
Qingwen Hu, Bernhard Lani-Wayda and Eugen Stumpf
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Preface: Analysis of cross-diffusion systems
Michael Winkler and Dariusz Wrzosek
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Stability of the heat and of the wave equations with boundary time-varying delays
Serge Nicaise, Julie Valein and Emilia Fridman
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Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators
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Claudianor O. Alves, M. M. Cavalcanti, Valeria N. Domingos Cavalcanti, Mohammad A. Rammaha and Daniel Toundykov
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A new finite element scheme for Landau-Lifchitz equations
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Birth of canard cycles
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Modeling the transmission dynamics of avian influenza with saturation and psychological effect
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Numerical investigation of Cattanneo-Christov heat flux in CNT suspended nanofluid flow over a stretching porous surface with suction and injection
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New exact solutions for some fractional order differential equations via improved sub-equation method
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Preface: New trends on numerical analysis and analytical methods with their applications to real world problems
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Generalised class of Time Fractional Black Scholes equation and numerical analysis
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Unsteady MHD slip flow of non Newtonian power-law nanofluid over a moving surface with temperature dependent thermal conductivity
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Professor Vicenţiu Rǎdulescu celebrates his sixtieth anniversary
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