ISSN:

1531-3492

eISSN:

1553-524X

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## Discrete & Continuous Dynamical Systems - B

April 2020 , Volume 25 , Issue 4

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**Abstract:**

In this paper, we introduce and study a new class of fractional differential hemivariational inequalities ((FDHVIs), for short) formulated by an initial-value fractional evolution inclusion and a hemivariational inequality in infinite Banach spaces. First, by applying measure of noncompactness, a fixed point theorem of a condensing multivalued map, we obtain the nonemptiness and compactness of the mild solution set for (FDHVIs). Further, we apply the obtained results to establish an existence theorem of the mild solution of a global attractor for the semiflow governed by a fractional differential hemivariational inequality ((FDHVI), for short). Finally, we provide an example to demonstrate the main results.

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**Abstract:**

In this paper we establish the nonlinear orbital instability of ground state standing waves for a Benney-Roskes/Zakharov-Rubenchik system that models the interaction of low amplitude high frequency waves, acustic type waves in

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**Abstract:**

We study the existence of the uniform global attractor for a family of infinite dimensional first order non-autonomous lattice dynamical systems of the following form:

with initial data

The nonlinear part of the system

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**Abstract:**

We derive characteristic functions to determine the number and stability of relaxation oscillations for a class of planar systems. Applying our criterion, we give conditions under which the chemostat predator-prey system has a globally orbitally asymptotically stable limit cycle. Also we demonstrate that a prescribed number of relaxation oscillations can be constructed by varying the perturbation for an epidemic model studied by Li et al. [SIAM J. Appl. Math, 2016].

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**Abstract:**

In this work, we consider the regularity property of stochastic convolutions for a class of abstract linear stochastic retarded functional differential equations with unbounded operator coefficients. We first establish some useful estimates on fundamental solutions which are time delay versions of those on

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**Abstract:**

We investigate the long-time behavior of solutions for the suspension bridge equation when the forcing term containing some hereditary characteristic. Existence of pullback attractor is shown by using the contractive function methods.

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**Abstract:**

We study a global well-posedness and asymptotic dynamics of measure-valued solutions to the kinetic Winfree equation. For this, we introduce a second-order extension of the first-order Winfree model on an extended phase-frequency space. We present the uniform(-in-time) **200** words.

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**Abstract:**

In this paper, by using the Gal

*+*[Abstract](1522)

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We study the ergodicity of non-autonomous discrete dynamical systems with non-uniform expansion. As an application we get that any uniformly expanding finitely generated semigroup action of

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In this paper, we study the existence of periodic solutions for a class of differential-algebraic equation

where

*+*[Abstract](1204)

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**Abstract:**

One of the simplest model of immune surveillance and neoplasia was proposed by Delisi and Resigno [

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**Abstract:**

We present a model for the dynamics of elastic or poroelastic bodies with monopolar repulsive long-range (electrostatic) interactions at large strains. Our model respects (only) locally the non-self-interpenetration condition but can cope with possible global self-interpenetration, yielding thus a certain justification of most of engineering calculations which ignore these effects in the analysis of elastic structures. These models necessarily combines Lagrangian (material) description with Eulerian (actual) evolving configuration evolving in time. Dynamical problems are studied by adopting the concept of nonlocal nonsimple materials, applying the change of variables formula for Lipschitz-continuous mappings, and relying on a positivity of determinant of deformation gradient thanks to a result by Healey and Krömer.

*+*[Abstract](1724)

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**Abstract:**

By employing Leray-Schauder alternative theorem of set-valued maps and non-Lyapunov method (non-smooth analysis, inequality analysis, matrix theory), this paper investigates the problems of periodicity and stabilization for time-delayed Filippov system with perturbation. Several criteria are obtained to ensure the existence of periodic solution of time-delayed Filippov system by using differential inclusion. By designing appropriate switching state-feedback controller, the asymptotic stabilization and exponential stabilization control of Filippov system are realized. Applying these criteria and control design method to a class of time-delayed neural networks with perturbation and discontinuous activation functions under a periodic environment. The developed theorems improve the existing results and their effectiveness are demonstrated by numerical example.

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**Abstract:**

This paper is concerned with the existence and asymptotic behavior of traveling wave solutions for a nonlocal dispersal vaccination model with general incidence. We first apply the Schauder's fixed point theorem to prove the existence of traveling wave solutions when the wave speed is greater than a critical speed

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**Abstract:**

This article discusses the spread of rumors in heterogeneous networks. Using the probability generating function method and the approximation theory, we establish an SICR rumor model and calculate the threshold conditions for the outbreak of the rumor. We also compare the speed of the rumors spreading with different initial conditions. The numerical simulations of the SICR model in this paper fit well with the stochastic simulations, which means that the model is reliable. Moreover the effects of the parameters in the model on the transmission of rumors are studied numerically.

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**Abstract:**

Our purpose is to formulate an abstract result, motivated by the recent paper [

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**Abstract:**

Efficient Legendre dual-Petrov-Galerkin methods for solving odd-order differential equations are proposed. Some Sobolev bi-orthogonal basis functions are constructed which lead to the diagonalization of discrete systems. Accordingly, both the exact solutions and the approximate solutions can be represented as infinite and truncated Fourier-like series. Numerical results indicate that the suggested methods are extremely accurate and efficient, and suitable for the odd-order equations.

*+*[Abstract](1404)

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**Abstract:**

This work provides a finite dimensional reducing and a smooth approximating for a class of stochastic partial differential equations with an additive white noise. Using the invariant random cone to show the asymptotical completion, this stochastic partial differential equation is reduced to a stochastic ordinary differential equation on a random invariant manifold. Furthermore, after deriving the finite dimensional reducing for another stochastic partial differential equation driven by a Wong-Zakai scheme via a smooth colored noise, it is proved that when the smooth colored noise tends to the white noise, the solution and the finite dimensional reducing of the approximate system converge pathwisely to those of the original system.

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**Abstract:**

This paper has two parts. In part Ⅰ, existence and uniqueness theorem is established for solutions of neutral stochastic differential equations with variable delays driven by

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**Abstract:**

In this paper, we extend our previous work on optimal control applied in an anthrax outbreak in wild animals. We use a system of ordinary differential equation (ODE) and partial differential equations (PDEs) to track the change in susceptible, infected and vaccinated animals as well as the infected carcasses. In addition to the assumption that the infected animals and the infected carcasses are the main source of infection, we consider the animal movement by diffusion and see its effects in disease transmission. Two controls: vaccinating susceptible animals and disposing infected carcasses properly are applied in the model and these controls depend on both space and time. We formulate an optimal control problem to investigate the effect of intervention strategies in our spatio-temporal model in controlling the outbreak at minimum cost. Finally some numerical results for the optimal control problem are presented.

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