A two-step algorithm for layout optimization of structures with discrete variables
Lianshuan Shi Enmin Feng Huanchun Sun Zhaosheng Feng
Journal of Industrial & Management Optimization 2007, 3(3): 543-552 doi: 10.3934/jimo.2007.3.543
This paper presents a mathematical model for Layout optimization of structure with discrete variables. The optimization procedure is composed of two kinds of sub-procedures of optimization: the topological optimization and the shape optimization. In each one, a comprehensive algorithm is used to treat the problem. The two kinds of optimization procedures are used in turn until convergence appears. After the dimension of the structure is reduced, the delimiting combinatorial algorithm is used to search for the better objective value. A couple of classical examples are presented to show the efficiency of the method. Numerical results indicate that the method is efficient and the optimal results are satisfactory.
keywords: delimiting and combinatorial algorithm structural optimization layout optimization Discrete variable relative difference quotient.
Zhaosheng Feng Wei Feng
Discrete & Continuous Dynamical Systems - S 2014, 7(6): i-i doi: 10.3934/dcdss.2014.7.6i
As we all know, many biological and physical systems, such as neuronal systems and disease systems, are featured by certain nonlinear and complex patterns in their elements and networks. These phenomena carry significant biological and physical information and regulate down-stream mechanism in many instances. This issue of Discrete and Continuous Dynamical Systems, Series S, comprises a collection of recent works in the general area of nonlinear differential equations and dynamical systems, and related applications in mathematical biology and engineering. The common themes of this issue include theoretical analysis, mathematical models, computational and statistical methods on dynamical systems and differential equations, as well as applications in fields of neurodynamics, biology, and engineering etc.
    Research articles contributed to this issue explore a large variety of topics and present many of the advances in the field of differential equations, dynamical systems and mathematical modeling, with emphasis on newly developed theory and techniques on analysis of nonlinear systems, as well as applications in natural science and engineering. These contributions not only present valuable new results, ideas and techniques in nonlinear systems, but also formulate a few open questions which may stimulate further study in this area. We would like to thank the authors for their excellent contributions, the referees for their tireless efforts in reviewing the manuscripts and making suggestions, and the chief editors of DCDS-S for making this issue possible. We hope that these works will help the readers and researchers to understand and make future progress in the field of nonlinear analysis and mathematical modeling.
Traveling wave solutions in parametric forms for a diffusion model with a nonlinear rate of growth
Zhaosheng Feng Goong Chen
Discrete & Continuous Dynamical Systems - A 2009, 24(3): 763-780 doi: 10.3934/dcds.2009.24.763
In this paper, we study a model of insect and animal dispersal where both density-dependent diffusion and nonlinear rate of growth are present. We analyze the existence of bounded traveling wave solution under certain parametric conditions by using the qualitative theory of dynamical systems. An explicit traveling wave solution is obtained by means of the first integral method. Traveling wave solutions in parametric forms for three particular cases are established by the Lie symmetry method.
keywords: Lie symmetry. equilibrium point infinitesimal generator traveling waves center manifold Fisher equation prolonged operator first integral
Stability of non-monotone non-critical traveling waves in discrete reaction-diffusion equations with time delay
Zhao-Xing Yang Guo-Bao Zhang Ge Tian Zhaosheng Feng
Discrete & Continuous Dynamical Systems - S 2017, 10(3): 581-603 doi: 10.3934/dcdss.2017029

This paper is concerned with traveling waves for temporally delayed, spatially discrete reaction-diffusion equations without quasi-monotonicity. We first establish the existence of non-critical traveling waves (waves with speeds c>c*, where c* is minimal speed). Then by using the weighted energy method with a suitably selected weight function, we prove that all noncritical traveling waves Φ(x+ct) (monotone or nonmonotone) are time-asymptotically stable, when the initial perturbations around the wavefronts in a certain weighted Sobolev space are small.

keywords: Spatially discrete reaction-diffusion equations non-monotone traveling waves stability weighted energy
Approximate solution of the Burgers-Korteweg-de Vries equation
Zhaosheng Feng Yu Huang
Communications on Pure & Applied Analysis 2007, 6(2): 429-440 doi: 10.3934/cpaa.2007.6.429
In this paper, we discuss the Liouville integrability of the Burgers-Korteweg-de Vries equation under certain parametric condition. An approximate solution is obtained by means of the Adomian decomposition method.
keywords: integrating factor decomposition method. approximate solution Traveling wave differential operator Burgers-KdV equation
Zhaosheng Feng Jinzhi Lei
Discrete & Continuous Dynamical Systems - B 2011, 16(2): i-iv doi: 10.3934/dcdsb.2011.16.2i
This issue of Discrete and Continuous Dynamical Systems–Series B, is dedicated to our professor and friend, Qishao Lu, on the occasion of his 70th birthday and in honor of his important and fundamental contributions to the fields of applied mathematics, theoretical mechanics and computational neurodynamics. His pleasant personality and ready helpfulness have won our hearts as his admirers, students, and friends.

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Periodic solutions for $p$-Laplacian systems of Liénard-type
Wenbin Liu Zhaosheng Feng
Communications on Pure & Applied Analysis 2011, 10(5): 1393-1400 doi: 10.3934/cpaa.2011.10.1393
In this paper, we study the existence of periodic solutions for $n-$dimensional $p$-Laplacian systems by means of the topological degree theory. Sufficient conditions of the existence of periodic solutions for $n-$dimensional $p$-Laplacian systems of Liénard-type are presented.
keywords: topological degree Liénard equation. existence $p$--Laplacian system periodic solution
A periodic and diffusive predator-prey model with disease in the prey
Xiaoling Li Guangping Hu Zhaosheng Feng Dongliang Li
Discrete & Continuous Dynamical Systems - S 2017, 10(3): 445-461 doi: 10.3934/dcdss.2017021

In this paper, we are concerned with a time periodic and diffusivepredator-prey model with disease transmission in the prey. Firstwe consider a $ SI $ model when the predator species is absent. Byintroducing the basic reproduction number for the $ SI $ model, weshow the sufficient conditions for the persistence and extinctionof the disease. When the presence of the predator is taken intoaccount, a number of sufficient conditions for the co-existence ofthe prey and predator species, the global extinction of predatorspecies and the global extinction of both the prey and predatorspecies are given.

keywords: Seasonality reaction-diffusion equations predator-prey model disease uniform persistence global extinction
Duffing-van der Pol-type oscillator systems
Zhaosheng Feng
Discrete & Continuous Dynamical Systems - S 2014, 7(6): 1231-1257 doi: 10.3934/dcdss.2014.7.1231
In this paper, under certain parametric conditions we are concerned with the first integrals of the Duffing-van der Pol-type oscillator system, which include the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. After applying the method of differentiable dynamics to analyze the bifurcation set and bifurcations of equilibrium points, we use the Lie symmetry reduction method to find two nontrivial infinitesimal generators and use them to construct canonical variables. Through the inverse transformations we obtain the first integrals of the original oscillator system under the given parametric conditions, and some particular cases such as the damped Duffing equation and the van der Pol oscillator system are included accordingly.
keywords: autonomous system Lie symmetry infinitesimal generator bifurcation Van der Pol oscillator first integral Duffing equation diffeomorphism.
Zhaosheng Feng Wei Feng
Communications on Pure & Applied Analysis 2011, 10(5): i-ii doi: 10.3934/cpaa.2011.10.5i
This issue of Communications on Pure and Applied Analysis, comprises a collection in the general area of nonlinear systems and analysis, and related applications in mathematical biology and engineering. During the past few decades people have seen an enormous growth of the applicability of dynamical systems and the new developments of related dynamical concepts. This has been driven by modern computer power as well as by the discovery of advanced mathematical techniques. Scientists in all disciplines have come to realize the power and beauty of the geometric and qualitative techniques developed during this period. More importantly, they have been able to apply these techniques to a various nonlinear problems ranging from physics and engineering to biology and ecology, from the smallest scales of theoretical particle physics up to the largest scales of cosmic structure. The results have been truly exciting: systems which once seemed completely intractable from an analytical point of view can now be studied geometrically and qualitatively. Chaotic and random behavior of solutions of various systems is now understood to be an inherent feature of many nonlinear systems, and the geometric and numerical methods developed over the past few decades contributed significantly in those areas.

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