一类具有饱和发生率的SIVS吸毒模型的动力学分析

本文研究一类具有饱和传染率的SIVS传染病模型.首先利用Routh-Hurwitz判据和特征根方法,得到平衡点的局部渐近稳定性,其次证明系统的持久性和无病平衡点的全局渐近稳定性,并利用极限系统理论得到地方病平衡点的全局渐近稳定性.最后用数值模拟验证理论结果的正确性.     

一类多因素HIV模型的研究

研究了一类多因素HIV模型.建立了一个标准型的DI模型,证明了无病平衡点的局部渐近稳定性和全局渐近稳定性.     

一类具有Beddington-DeAngelis响应函数的阶段结构捕食模型的稳定性

该文讨论一类具有Beddington-DeAngelis响应函数的阶段结构捕食模型.利用RouthHurwitz判别定理讨论了其正常数平衡解的局部渐近稳定性,通过构造Lyapunov函数方法得到了全局渐近稳定性.     

具有时滞的Lotka-Volterra食饵-捕食者成年种群模型的稳定性分析

本文主要考虑具有时滞的Lotka-Volterra食饵-捕食者成年种群模型.首先,通过线性化方法和分析特征根在复平面上的分布情况,获得了系统边界平衡点的局部渐近稳定性;其次,利用比较原理和上下解方法证明了半平凡平衡点和共存平衡点的全局渐近稳定性.     

带有标准发生率和信息干预的时滞SIRS传染病模型的稳定性分析

本文考虑一类具有标准发生率和信息干预的时滞SIRS传染病模型.通过分析模型的特征方程,讨论无病平衡点和地方病平衡点局部渐近稳定性.应用Halanay不等式对无病平衡点的全局渐近稳定性进行证明.通过构造适当的Lyapunov函数讨论地方病平衡点全局渐近稳定性.最后通过数值模拟分析一些重要参数对疾病传播的影响.     

耗散稀薄气体的动力学模型的L1渐近稳定性

本文讨论了一种具有非弹性碰撞的麦克斯韦分子模型,首先利用傅立叶变换的方法分析该模型的自型解在特殊范数下的渐近稳定性,然后通过引入的Sobolev空间,证明该自型解在L1范数下的渐近稳定性.     

带Beddington-DeAngelis功能反应项的捕食者-食饵扩散模型的稳定性

本文首先应用上下解方法讨论一类带Beddington-DeAngelis功能反应项的捕食者-食饵扩散模型解的一致有界性和整体存在性,然后通过线性化方法分别给出该模型的半平凡平衡点和正平衡点局部渐近稳定的充分条件,最后应用Lyapunov泛函方法讨论唯一正平衡点的全局渐近稳定性.     

一类潜伏期和染病期均具有传染性的手足口病模型

根据手足口病的病理特性及传播特点,建立一类描述其传播的数学模型并对模型的动力学性态进行分析.首先利用再生矩阵的方法定义了模型的基本再生数R_0,同时通过构造Lyapunov函数和Routh-Hurwitz判据证明了当R_0≤1时无病平衡点E_0的金局渐近稳定性,R_0>1时地方病平衡点E_*的局部渐近稳定性,并进一步证明了在一定条件下地方病平衡点的全局渐近稳定性.     

一类具时滞SIR传染病模型的动力行为

分析传染病模型的稳定性,并考虑到已感染者对易感染者的作用的时滞影响.文中首先在R_01时,构造一个Lyapunov泛函,证明了无病平衡点的全局渐近稳定性.当R_01时,证明了正平衡点的局部渐近稳定性和持久性.     

线性广义系统时滞相关渐近稳定的一个新判据

研究线性广义时滞系统时滞相关的渐近稳定性问题.利用Lyapunov-Krasovskii泛函理论和自由权矩阵方法,得到严格线性矩阵不等式(LMI)形式的时滞相关渐近稳定新判据,并没有采用模型变换和界定交叉项方法.最后通过数值算例验证新判据的有效性.     

Asymptotic stability analysis of autonomous systems by applying the method of localization of compact invariant sets

The asymptotic stability and global asymptotic stability of equilibria in autonomous systems of differential equations are analyzed. Conditions for asymptotic stability and global asymptotic stability in terms of compact invariant sets and positively invariant sets are proved. The functional method of localization of compact invariant sets is proposed for verifying the fulfillment of these conditions. Illustrative examples are given.     

On Delay-Dependent Global Asymptotic Stability for Pendulum-Like Systems

This paper deals with global asymptotic stability for the delayed nonlinear pendulum-like systems with polytopic uncertainties. The delay-dependent criteria, guaranteeing the global asymptotic stability for the pendulum-like systems with state delay for the first time, are established in terms of linear matrix inequalities (LMIs) which can be checked by resorting to recently developed algorithms solving LMIs. Furthermore, based on the derived delay-dependent global asymptotic stability results, LMI characterizations are developed to ensure the robust global asymptotic stability for delayed pendulum-like systems under convex polytopic uncertainties. The new extended LMIs do not involve the product of the Lyapunov matrix and the system matrices. It enables one to check the global asymptotic stability by using parameter-dependent Lyapunov methods. Finally, a concrete application to phase-locked loop (PLL) shows the validity of the proposed approach.     

Dynamics of the density dependent predator-prey system with Beddington-DeAngelis functional response

Two models of a density dependent predator-prey system with Beddington-DeAngelis functional response are systematically considered. One includes the time delay in the functional response and the other does not. The explorations involve the permanence, local asymptotic stability and global asymptotic stability of the positive equilibrium for the models by using stability theory of differential equations and Lyapunov functions. For the permanence, the density dependence for predators is shown to give some negative effect for the two models. Further the permanence implies the local asymptotic stability for a positive equilibrium point of the model without delay. Also the global asymptotic stability condition, which can be easily checked for the model is obtained. For the model with time delay, local and global asymptotic stability conditions are obtained.     

Global asymptotic stability of a class of nonautonomous integro-differential systems and applications

In this paper, we study the global asymptotic stability of a class of nonautonomous integro-differential systems. By constructing suitable Lyapunov functionals, we establish new and explicit criteria for the global asymptotic stability in the sense of Definition 2.1. In the autonomous case, we discuss the global asymptotic stability of a unique equilibrium of the system, and in the case of periodic system, we establish sufficient criteria for existence, uniqueness and global asymptotic stability of a periodic solution. Also explored are applications of our main results to some biological and neural network models. The examples show that our criteria are more general and easily applicable, and improve and generalize some existing results.     

Global Behaviour of Solutions of Nonlinear Delay Difference Equations*

In this paper global asymptotic stability and asymptotic behaviour of solutions of nonlinear delay difference equations has been studied and a few sets of sufficient conditions for global asymptotic stability are derived.     

ON GLOBAL ASYMPTOTIC STABILITY OF THE ZERO SOLUTION OF A GENERALIZED LIENARD′S SYSTEM

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Global asymptotic stability analysis for integro-differential systems modeling neural networks with delays

In this paper, the global asymptotic stability of the equilibrium point of integro-differential systems modeling neural networks with time-varying delays are studied. Proper Lyapunov functionals and some analytic techniques are employed to derive the sufficient conditions under which the networks proposed are the global asymptotic stability. The results have shown to improve the previous global asymptotic stability results derived in the literature. Some examples are given to illustrate the correctness of our results.     

一类扩张的细胞神经网络稳定性判别法

本文研究一类含有阻尼项带有时滞细胞神经网络的全局渐进稳定性和一致稳定性的性质,通过构造适当的李雅普诺夫函数及利用分析的有关知识,给出了全局渐进稳定性和一致稳定的判别法．     

Stability and stabilization of a class of nonlinear impulsive hybrid systems based on FSM with MDADT

The issue of stability and stabilization for a class of nonlinear impulsive hybrid systems based on finite state machine (FSM) with mode-dependent average dwell time (MDADT) is investigated in this paper. The concepts of global asymptotic stability and global exponential stability are extended for the systems, and the multiple Lyapunov functions (MLFs) are constructed to prove the sufficient conditions of global asymptotic stability and global exponential stability, respectively. Furthermore, the method of stabilization is also given for the hybrid systems. The application of MLFs and MDADT leads to a reduction of conservativeness in contrast with classical Lyapunov function. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed approach.     

Global asymptotic behavior in a Lotka–Volterra competition system with spatio-temporal delays

This paper is concerned with a Lotka–Volterra competition system with spatio-temporal delays. By using the linearization method, we show the local asymptotic behavior of the nonnegative steady-state solutions. Especially, the global asymptotic stability of the positive steady-state solution is investigated by the method of upper and lower solutions. The result of global asymptotic stability implies that the system has no nonconstant positive steady-state solution.