Unconditional global exponential stability in Lagrange sense of genetic regulatory networks with SUM regulatory logic

In this paper, the global exponential stability in Lagrange sense for genetic regulatory networks (GRNs) with SUM regulatory logic is firstly studied. By constructing appropriate Lyapunov-like functions, several criteria are presented for the boundedness, ultimate boundedness and global exponential attractivity of GRNs. It can be obtained that GRNs with SUM regulatory logic are unconditionally globally exponentially stable in Lagrange sense. These results can be applied to analyze monostable as well as multistable networks. Furthermore, to analyze the stability for GRNs more comprehensively, the existence of equilibrium point of GRNs is proved, and some sufficient conditions of the global exponential stability in Lyapunov sense for GRNs are derived. Finally two numerical examples are given to illustrate the application of the obtained results.     

具有时滞的Schoener模型的全局稳定性

研究了具有时滞的Schoener竞争模型,通过构造一个合理的lyapunov函数,在一定条件下得到了该系统正解的全局稳定性．     

多时滞三种群捕食模型的持久性和全局渐近性

研究了一类多时滞非自治三种群捕食模型的持久性和全局渐近稳定性,分别利用比较原理和构造Lyapunov函数方法得到了模型持久生存与全局渐近稳定性的充分条件,并举例说明定理的可行性且利用Matlab绘出图像.     

具有扩散的n-斑块单种群系统的全局稳定性

研究了具有扩散的ｎ－斑块多种环境下单种群非自治模型,在假定该模型所有系数连续有界的情况下,得到了系统全局稳定的充分条件。     

具有时滞和反馈控制的非自治Schoner模型的持续生存与全局渐近稳定性

讨论了具有时滞和反馈控制的非自治Schoner模型,得到了系统一致持续生存和全局渐近稳定的充分条件．     

一个具有时滞和反馈控制的单种群模型的全局稳定性

研究一个具有时滞和反馈控制的单种群模型,通过构造适当的Lyapunov泛函,得到了保证系统的一个正平衡点全局渐近稳定的充分条件,并对一个实例进行了数值模拟。     

Global stability and persistence in LG–Holling type II diseased predator ecosystems

A Leslie–Gower–Holling type II model is modified to introduce a contagious disease in the predator population, assuming that disease cannot propagate to the prey. All the system’s equilibria are determined and the behaviour of the system near them is investigated. The main mathematical issues are global stability and bifurcations for some of the equilibria, together with sufficient conditions for persistence of the ecosystem. Counterintuitive results on the role played by intraspecific competition are highlighted.     

Robust stability of genetic regulatory networks with distributed delay

This paper investigates robust stability of genetic regulatory networks with distributed delay. Different from other papers, distributed delay is induced. It says that the concentration of macromolecule depends on an integral of the regulatory function of over a specified range of previous time, which is more realistic. Based on Lyapunov stability theory and linear matrix inequality (LMI), sufficient conditions for genetic regulatory networks to be global asymptotic stability and robust stability are derived in terms of LMI. Two numerical examples are given to illustrate the effectiveness of our theoretical results.     

一类具有标准发生率的SIS型传染病模型的全局稳定性

研究一类具有标准发生率的SIS传染病模型,讨论了各类平衡点存在的条件;运用微分方程的定性理论,得到了无病平衡点E_1和地方病平衡点E_2的全局渐近稳定的充分条件.     

Periodic solution of a chemostat model with Beddington-DeAnglis uptake function and impulsive state feedback control

In this paper, a chemostat model with Beddington-DeAnglis uptake function and impulsive state feedback control is considered. We obtain sufficient conditions of the global asymptotical stability of the system without impulsive state feedback control. We also obtain that the system with impulsive state feedback control has periodic solution of order one. Sufficient conditions for existence and stability of periodic solution of order one are given. In some cases, it is possible that the system exists periodic solution of order two. Our results show that the control measure is effective and reliable.     

具有时滞的双向联想记忆神经网络的全局渐近稳定性

双向联想记忆模型是两层异联想网络,本文讨论了具有轴突信号传输时滞的双向联想记忆神经网络的全局渐近稳定性,得出了保证神经网络平衡点稳定的几个充分条件,所得到的结论对于具有时滞的连续双向联想记忆神经网络的设计和应用都是很有意义的。     

STABLE POSITIVE SOLUTION OF THE NONAUTONOMOUS LOTKA-VOLTERRA MUTUALISTIC SYSTEM

l！ntroductionAutonomousLotka－VolterramutuallstlcsystemhasbeenstudiedInmanypaperE3】,E4］．［5】,ourpurposehereIstoconsiderthenonautonomouStwo－SPPCllsLOtkt－Volterramutuallstlcsystem．WeareconcernedwiththedifferentialequationsbelongtoC‘andC‘isthesetOfsllCOlltlnuouSfunCtionSg：［0,＋。）、RbOUnded。hove。ndbelOWbyCOnst。ms,moreover,notallofa：。（t）（l＜l,j＜n,。／j）arezero．Theper。odlccasehasbeenconsideredIn［1】．Insection3ofthlspaper,westudiedthegeneralcaseoftlmede…     

一类含分布时滞的流行病模型的研究

提出了一类含分布时滞的流行病模型,利用构造李亚普诺夫泛函的方法,得到了无病平衡点和地方病平衡点全局稳定性的结论,揭示了平均时滞对各类平衡点稳定性的影响。     

基于反馈控制离散Lotka-Volterra竞争模型的持续生存和稳定性

针对一类具有偏离自变量的离散Lotka-Volterra竞争模型,考虑到不可避免的外界扰动,通过引入反馈控制,基于一定的分析技巧得到该系统持久性与全局稳定性的充分条件.生态意义上表明:在外界扰动下,具有偏离自变量的离散Lotka-Volterra竞争模型仍能持续生存并保持全局稳定发展.     

单种群扩散时滞系统的持久性和全局渐近稳定性

在这篇文章中,我们证明了一个单种群扩散时滞系统的持久性,同时,给出它的全局渐近稳定性的充分条件。     

变时延神经网络的全局指数稳定性及收敛性

利用Lyapunov泛函方法和线性矩阵不等式（LMI）技术,通过引入一系列参数,给出全局指数稳定的平衡点的判别条件和时延的最大上界和神经网络的收敛速度,所得结果较之一些文献中的结果简单、实用并且对于具体设计带时延神经网络有重要的指导意义.最后,通过实例表明给出的判定条件是有效、可行的.     

离散型二维竞争系统的渐近稳定性

研究了离散型二维竞争系统的渐近稳定性,得到了这类生物模型关于正平衡点渐近稳定的一系列充分条件。     

Permanence and Global Stability for Two-Species Cooperative System with Time Delays in Two-Patch Environment

IIntroductionA。ebasicandimport。tbiologicalquestiontoaskiswhetherornotthOSein、Ivedpopu－lati。willbealiveandwellinthelOng。Therefore，po～ceand印出llityofag。Sys－temareInterestingandimPO～bilolgitallyaswellasInathernatically．Sincethep；oneerlflgtheoretitalworkbyShell—t‘），－yworkshwe由以旧dmtheeffectof叩analfaCtOYswhi山playacrucialroleinpennanenceandst北ilityOfp水＂lations．Infa戊，the山S严rsalbtweenpat山esdtenco。r。Inecologi］envi。t，and。er」lstlcmeddssh讪dincludethedisp四油p…     

具有Holling Ⅱ类功能反应且周期系数的三种群混和模型的研究

研究三种群之间既有捕食关系又有竞争关系的混和模型,同时捕食者有ＨｏｌｌｉｎｇⅡ类功能反应,得到唯一存在全局渐近稳定周期的条件。