Step-like contrast structure for a quasilinear system of singularly perturbed differential equations with a zero characteristic number

We consider a system of singularly perturbed first-order differential equations with a zero characteristic number. The solution of such a problem is characterized by the presence of a contrast structure, that is, of an internal transition layer on a given interval. We prove the existence of an exact solution with a step-like contrast structure and construct its uniform asymptotic expansion. An example is given.     

THE STABILITY IN NEURAL NETWORK WITH DELAY AND DYNAMICAL THRESHOLDEFFECTS

1 IntroductionThe researches on dynamics of neural network systems have been arousinga great deal of interests for more than thirty years. In last ten years, many.researches focused on the study of dynamics of neural network models withdelay. In fact, neural networks often have times delay in reality, for exampledue to the finite switching speed of amplifiers in electronic neural networks.Thus, a large amount of excellent results appeared consecutively [1]--[5]. In thispaper, what we study is…     

Step-like contrast structure for a nonlinear system of singularly perturbed differential equations in the critical case

For an n-dimensional singularly perturbed system of differential equations, we construct the asymptotics of a solution with a step-like contrast structure in the critical case. We prove the existence of a solution and obtain an estimate for the remainder terms of the asymptotic representation of this solution.     

Periodic contrast structures in systems of the reaction-diffusion-advection type

In the present paper, we consider a nonlinear parabolic problem for an equation that is referred in applications to as the reaction-diffusion-advection equation and whose solutions have internal transition layers (contrast structures). For such equations, we construct the asymptotics of arbitrary-order accuracy and prove the existence and the Lyapunov stability.     

Dynamics analysis of a reaction–diffusion system with Beddington–DeAngelis functional response and strong Allee effect

In this paper, the dynamics of a diffusive predator–prey model with modified Leslie–Gower term and strong Allee effect on prey under homogeneous Neumann boundary condition is considered. Firstly, we obtain the qualitative properties of the system including the existence of the global positive solution and the local and global asymptotical stability of the constant equilibria. In addition, we investigate a priori estimate and the nonexistence of nonconstant positive steady state solutions. Finally, we establish the existence and local structure of steady state patterns and time-periodic patterns for the system.     

对高维热粘弹方程组解的整体存在性的注记

In this paper, we obtain some global existence results for the higher-dimensional nonhomogeneous, linear, semilinear and nonlinear thermoviscoelastic systems by using semi-group approach.     

一类泛函微分方程周期正解的存在性

本文研究了一类带参数的高维泛函微分程(1.1)的周期正解的存在性.利用一个著名的不动点指标定理,获得了该方程周期正解的存在性、多重性和不存在性.     

Asymptotical behavior of ground state solutions for critical quasilinear Schrödinger equation

This paper is concerned with the existence and asymptotical behavior of positive ground state solutions for a class of critical quasilinear Schrodinger equation.By using a change of variables and variational argument,we prove the existence of positive ground state solution and discuss their asymptotical behavior。     

Positive solutions of a diffusive Leslie–Gower predator–prey model with Bazykin functional response

In this paper, we consider a diffusive Leslie–Gower predator–prey model with Bazykin functional response and zero Dirichlet boundary condition. We show the existence, multiplicity and uniqueness of positive solutions when parameters are in different regions. Results are proved by using bifurcation theory, fixed point index theory, energy estimate and asymptotical behavior analysis.     

Positive steady state solutions of a Leslie–Gower predator–prey model with Holling type II functional response and density-dependent diffusion

In this paper, we consider a Leslie–Gower predator–prey model with Holling type II functional response and density-dependent diffusion under zero Dirichlet boundary condition. Using degree theory, bifurcation theory, energy estimates and asymptotical behavior analysis, the existence and multiplicity of positive steady state solutions were shown under certain conditions on the parameters.     

Asymptotic behavior of the expected optimal value of the multidimensional assignment problem

The Multidimensional Assignment Problem (MAP) is a higher-dimensional version of the Linear Assignment Problem that arises in the areas of data association, target tracking, resource allocation, etc. This paper elucidates the question of asymptotical behavior of the expected optimal value of the large-scale MAP whose assignment costs are independent identically distributed random variables with a prescribed probability distribution. We demonstrate that for a broad class of continuous distributions the limiting value of the expected optimal cost of the MAP is determined by the location of the left endpoint of the support set of the distribution, and construct asymptotical bounds for the expected optimal cost.     

On the Existence of Markov Partitions for Zd Actions

The theory of higher-dimensional shifts of finite type is stilllargely an open area of investigation. Recent years have seenmuch activity, but fundamental questions remain unanswered.In this paper we consider the following basic question. Givena shift of finite type (SFT), under what topological mixingconditions are we guaranteed the existence of Bernoulli (oreven K, mixing, or weakly mixing) invariant measures?     

Stability and Hopf bifurcation analysis of an eco-epidemic model with a stage structure

In this paper, an eco-epidemiological model with a stage structure is considered. The asymptotical stability of the five equilibria, the existence of stability switches about positive equilibrium, is investigated. It is found that Hopf bifurcation occurs when the delay τ passes though a critical value. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given.     

具有人口年龄结构的Solow-Swan模型与仿真

本文中,我们将人口年龄结构引入经典的Solow-Swan模型,探讨人口年龄结构变动对经济增长的影响.利用比较定理证明当人口趋于稳定的人口结构时刻划模型的微分方程的解是渐近稳定的.通过数值仿真,我们看到经济增长在少年抚养下降时加速,在老年抚养上升时减缓.在人口转变时期存在"人口红利",人口老龄化导致的劳动力人数占人口的比重下降会使经济增长减缓甚至下降.     

Pullback attractors for the non-autonomous Benjamin-Bona-Mahony equations in H

In this paper, we prove the existence of the pullback attractor for the non-autonomous Benjamin-Bona-Mahony equations in H² by establishing the pullback uniformly asymptotical compactness.     

The ergodic theorem for Markov processes

Most of the material in Sections 4-5-6-8-11 has been published in [4]-[10]. We shall deal with the asymptotical behavior of the iterates of a Markov transition function. Our aim is to generalize the results about the ‘cyclic’ convergence of the iterates of a Markov matrix. Throughout the paper functional analytic methods are used and not probabilistic arguments. The report is self contained, modulo standart results from functional analysis, except for the decomposition into conservative and dissipative parts. Also we assume the existence of an invariant σ finite measure on the conservative part. This has been proved, under some restrictions, by several authors using probabilistic methods. The research reported in this document has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR 66-18, through the European Office of Aerospace Research (OAR) United States Air Force.     

Periodic solution and reflective function of higher-dimensional differential systems

In this article, we apply the theory of reflecting function to discuss the existence and stability of periodic solution of higher-dimensional nonlinear nonautonomous differential systems.     

The existence of a random attractor for the three dimensional damped Navier–Stokes equations with additive noise

This article is concerned with the asymptotical behavior of solutions for the three-dimensional damped Navier–Stokes equations with additive noise. Due to the shortage of the existence proof of the existence of random absorbing sets in a more regular phase space, we cannot obtain some kind of compactness of the cocycle associated with the three-dimensional damped Navier–Stokes equations with additive noise by the Sobolev compactness embedding theorem. In this paper, we prove the existence of a random attractor for the three-dimensional damped Navier–Stokes equations with additive noise by verifying the pullback flattening property.     

Traveling wavefronts for a two-species predator–prey system with diffusion terms and stage structure

In this paper, we considered an important model describing a two-species predator–prey system with diffusion terms and stage structure. By using the linearized method, we investigated the locally asymptotical stability of the nonnegative equilibria of the system and obtained the locally stable conditions. And by using the approach introduced by Canosa [J. Canosa, On a nonlinear diffusion equation describing population growth, IBM J. Res. Dev. 17 (1973) 307–313] and the method of upper and lower solutions, we studied the existence of traveling wavefronts, connecting the zero solution with the positive equilibrium of the system. Our results show that the traveling wavefronts exist and appear to be monotone. Finally, we given a conclusion to summarize the overall achievements of the work presented in the paper.     

三点粗异宿环分支

本文研究高维系统连接三个鞍点的粗异宿环的分支问题.在一些横截性条件和非扭曲条件下,获得了Γ附近的1-异宿三点环, 1-异宿两点环、 1-同宿环和1-周期轨的存在性,唯一性和不共存性.同时给出了分支曲面和存在域.上述结果被进一步推广到连接l个鞍点的异宿环的情况,其中l≥2.