一类具脉冲效应的竞争生态数学模型的持久性和渐进行为

研究了一类具有脉冲效应的非自治Lotka-Valterra竞争生态数学模型系统,运用李雅普诺夫函数和比较定理,给出了系统的持久性和渐进行为的充分条件.     

具有功能反应的脉冲型捕食系统的周期解

考虑具有脉冲效应和sigmoid功能反应的非自治捕食系统,利用重合度理论研究了系统正周期解的存在性,建立了存在正周期解的充分条件.     

具有脉冲效应非自治捕食系统的研究

研究了具有脉冲效应的非自治捕食系统,该系统是两个具有互惠关系的食饵种群被一个捕食种群捕食.利用重合度理论证明系统正周期解的存在性.     

一类具有脉冲效应的非线性竞争系统的持久及全局吸引性(英文)

通过利用常微分方程比较定理以及构造恰当Lyapounov泛函,研究了一类具有脉冲效应的广义非自治n种群Gilpin-Ayala竞争系统,给出了使系统正解持久以及全局吸引的充分性条件,所得结论改进并推广了一些现有结果.     

具脉冲效应和反馈控制的企业集群竞争模型的持久性分析

根据企业集群与生物种群有着一定的相似性,借鉴种群生态学中的种群竞争模型建立了网状型企业集群模式下企业间竞争关系的数学模型-一类具脉冲效应和反馈控制的非自治企业竞争模型系统,并通过脉冲微分方程的比较性定理,建立了该系统持久性生存的充分条件,并做经济学解释.     

具有脉冲效应的灰色随机时滞系统的鲁棒稳定性

研究了一类具有脉冲效应和时变时滞的灰色随机系统的鲁棒稳定性问题。在给出了脉冲随机泛函微分系统随机稳定性的条件的基础上,首先利用Lyapunov-KrasoVskii泛函法和灰矩阵的连续矩阵覆盖的分解技术,得到了具有脉冲效应和时变时滞的灰色随机系统的随机鲁棒稳定性判据,进而基于所得的这个随机鲁棒稳定性判据和Dini导数,给出了该系统指数鲁棒稳定性的判据。实例表明,所得判据是有效的和实用的。     

一类非自治随机时滞系统的状态反馈镇定

本文讨论一类非自治随机时滞系统的状态反馈镇定问题.一方面,考虑到模型的特征(复杂非线性、随机以及非自治),本文在反步框架下设计随机时滞系统的时变反馈控制器,给出相应的状态反馈控制策略;另一方面,基于随机Razumikhin稳定性理论来分析系统的依概率全局渐近稳定性,放宽了系统镇定对时滞项的要求.最后,利用数值仿真验证了反馈控制器及控制策略的有效性.     

具有环境污染的随机Lotka-Volterra模型周期解的存在性与种群的灭绝性

种群系统在受到环境噪声干扰的同时,还会受到环境污染的影响.讨论了具有环境污染的非自治随机Lotka-Volterra模型.通过构造Lyapunov函数证明了系统正周期解的存在性.运用Ito公式和鞅的强大数定律给出了种群灭绝的充分条件.通过数值例子验证了所得到的结论.     

具有Holling Ⅲ功能性反应的随机捕食食饵模型的平稳分布和周期解

该文研究了一类具有HollingⅢ功能性反应的随机捕食-食饵系统的动力学行为.对于自治系统,首先获得,对于任意的正初始值,系统都存在唯一的全局正解;第二,利用随机微分方程比较定理,得到系统的平均持续生存与灭绝的充分条件;第三,通过构造Lyapunov函数,证明了系统存在唯一的平稳分布且具有遍历性;而对于非自治系统,通过应用Has'mintskii定理证明了,系统至少存在一个非平凡的正周期解;最后,给出数值模拟来验证主要结果.     

一类具有脉冲效应和Beddington-DeAngelis功能函数的非自治随机捕食-被捕食系统

建立了一类具有Beddington-DeAngelis功能函数的非自治脉冲随机捕食-被捕食系统.通过It?公式和随机微分方程比较原理,证明了该系统解的存在唯一性和有界性以及系统趋于灭绝的条件.     

Dynamics analysis and numerical simulations of a stochastic non-autonomous predator–prey system with impulsive effects

In this paper, we propose a stochastic non-autonomous Lotka–Volterra predator–prey model with impulsive effects and investigate its stochastic dynamics. We first prove that the subsystem of the system has a unique periodic solution which is globally attractive. Furthermore, we obtain the threshold value in the mean which governs the stochastic persistence and the extinction of the prey–predator system. Our results show that the stochastic noises and impulsive perturbations have crucial effects on the persistence and extinction of each species. Finally, we use the different stochastic noises and impulsive effects parameters to provide a series of numerical simulations to illustrate the analytical results.     

Stability of impulsive stochastic differential delay systems and its application to impulsive stochastic neural networks

This paper is concerned with the stability of n-dimensional stochastic differential delay systems with nonlinear impulsive effects. First, the equivalent relation between the solution of the n-dimensional stochastic differential delay system with nonlinear impulsive effects and that of a corresponding n-dimensional stochastic differential delay system without impulsive effects is established. Then, some stability criteria for the n-dimensional stochastic differential delay systems with nonlinear impulsive effects are obtained. Finally, the stability criteria are applied to uncertain impulsive stochastic neural networks with time-varying delay. The results show that, this convenient and efficient method will provide a new approach to study the stability of impulsive stochastic neural networks. Some examples are also discussed to illustrate the effectiveness of our theoretical results.     

Stochastic asymptotical stability for stochastic impulsive differential equations and it is application to chaos synchronization

In this paper, the stochastic asymptotical stability of stochastic impulsive differential equations is studied, and a comparison theory about the stochastic asymptotical stability of trivial solution is established. From the comparison theory, we can find out whether the stochastic impulsive differential system is stochastic asymptotically stable by studying the stability of a deterministic comparison system. As an application of this theory, we study the problem of chaos synchronization in Chua circuit using impulsive method. Finally, numerical simulation is employed to verify the feasibility of our method.     

Global dynamics analysis of a nonlinear impulsive stochastic chemostat system in a polluted environment

This paper intends to develop a new method to obtain the threshold of an impulsive stochastic chemostat model with saturated growth rate in a polluted environment. By using the theory of impulsive differential equations and stochastic differential equations, we obtain conditions for the extinction and the permanence of the microorganisms of the deterministic chemostat model and the stochastic chemostat model. We develop a new numerical computation method for impulsive stochastic differential system to simulate and illustrate our theoretical conclusions. The biological results show that a small stochastic disturbance can cause the microorganism to die out, that is, a permanent deterministic system can go to extinction under the white noise stochastic disturbance. The theoretical method can also be used to explore the threshold of some impulsive stochastic differential equations.     

Stepanov-like pseudo almost periodic solutions for impulsive perturbed partial stochastic differential equations and its optimal control

This paper is mainly concerned with the Stepanov-like pseudo almost periodicity to a class of impulsive perturbed partial stochastic differential equations. Firstly, we prove the existence of $p$-mean piecewise Stepanov-like pseudo almost periodic mild solutions for the impulsive stochastic dynamical system in a Hilbert space under non-Lipschitz conditions. The results are obtained by using the fixed point techniques with fractional power arguments. Then the existence of optimal pairs of system governed by impulsive partial stochastic differential equations is also obtained. Finally, an example is provided to illustrate the developed theory.     

Periodic averaging method for impulsive stochastic differential equations with Lévy noise

The purpose of this paper is to present a periodic averaging method for impulsive stochastic differential equations with Lévy noise under non-Lipschitz condition. It is shown that the solutions of impulsive stochastic differential equations with Lévy noise converge to the solutions of the corresponding averaged stochastic differential equations without impulses     

Asymptotic behaviour of reaction–diffusion equations with non-damped impulsive effects

In this paper we consider non-autonomous reaction–diffusion systems with impulsive effects at fixed moments of time from the point of view of the theory of global attractors. For a translation-compact nonlinear term which does not provide the uniqueness of the Cauchy problem, and for different classes of non-damped multivalued impulse perturbations, we construct a multivalued non-autonomous dynamical system and prove for it the existence of a compact global attractor.     

使用T-20治疗HIV-1患者的不同策略的数学建模与研究

通过建立数学模型,描述了HIV-1感染者使用抗病毒治疗药物——融合酶抑制剂(T-20)的治疗效果．使用脉冲微分方程描述了T-20的使用过程,并考虑了两种不同的药物消除动力学:一级消除动力学与米-曼(Michaelis-Menten)消除动力学．此模型是个非自治微分方程系统,主要关注其无病平衡态,并研究当接受治疗者在服药完全依从的治疗过程中无病平衡态的稳定性．分别针对药物剂量与服药间隔得到了使得无病平衡态稳定的阈值条件．此外,还研究了间歇治疗的效果．研究表明,间歇治疗的效果甚至可以比完全不治疗还要糟糕．     

Using impulses to control the convergence toward invariant surfaces of continuous dynamical systems

Let us consider a smooth invariant surface S of a given ordinary differential equations system. In this work we develop an impulsive control method in order to assure that the trajectories of the controlled system converge toward the surface S. The method approach is based on a property of a certain class of invariant surfaces whose the dynamics associated to their transverse directions can be described by a non-autonomous linear system. This fact allows to define an impulsive system which drives the trajectories toward the surface S. Also, we set up a definition of local stability exponents which can be associated to such kind of invariant surface.