反馈控制Lotka-Volterra合作系统稳定性研究

研究具有反馈控制的两种群Lotka-Volterra合作系统正平衡点的稳定性.通过构造适当的Lyapunov函数得到一组保证正平衡点全局吸引的充分性条件.我们的结果表明在原系统存在正平衡点时,反馈控制变量仅能改变正平衡点的位置,而不会改变正平衡点的稳定性.     

一类具有非线性传染率的时滞SIR模型的分析

分析并建立具有时滞及非线性传染率的SIR传染病模型.通过分析在无病平衡点和正平衡点处的特征方程,可得到在这两个平衡点处的局部渐近稳定性,然后我们得到了系统在两个平衡点处的全局渐近稳定性,最后我们证明了系统的持久性.     

一类具有时滞的捕食——食饵系统的稳定性与Hopf分支

研究了一类具有时滞的捕食—食饵系统,通过分析正平衡点处的特征方程,讨论了系统正平衡点的稳定性;以时滞作为分支参数,应用Hopf分支理论,得到了系统存在Hopf分支的充分条件.     

一类带时滞的Watt型功能性反应的捕食系统的Hopf分支

研究一类具有时滞的Watt型功能性反应的捕食模型,通过分析正平衡点处的特征方程,讨论了该系统正平衡点的稳定性.应用Hopf分支理论,得到了该系统产生Hopf分支的条件.     

一类具收获率的功能性反应自抑制三种群模型定性分析

研究了一类具收获率的功能性反应自抑制三种群捕食模型,运用微分方程稳定性理论,确定了捕食系统模型的平衡点存在的条件和性态,得到了系统正平衡点渐近稳定条件,并且分析了平衡点的全局稳定性及系统持续生存的条件.最后利用Matlab软件进行了数值模拟验证.     

具反馈控制的一方不能独立生存偏利合作系统的稳定性

研究具反馈控制的一方不能独立生存的两种群偏利合作系统正平衡点和边界平衡点的稳定性,通过构造适当的Lyapunov函数分别得到保证正平衡点和边界平衡点全局渐近稳定的充分性条件,并通过MATLAB进行数值模拟.研究结果表明,在原系统存在正平衡点时,适当的反馈控制变量仅改变正平衡点的位置,不会改变正平衡点的稳定性;但不适当的反馈控制变量将导致系统中不能独立生存的种群绝灭.     

具反馈控制的单方不能独立生存合作系统稳定性研究

研究具有反馈控制的单方不能独立生存两种群合作系统正平衡点和边界平衡点的稳定性.通过构造适当的Ly印unov函数分别得到一组保证正平衡点和边界平衡点全局吸引的充分性条件.我们的结果表明在原系统存在唯一的全局吸引的正平衡点时,反馈控制变量控制在一定的范围,则所研究系统仍然具有唯一的全局吸引的正平衡点;反馈控制变量足够大,则第二个种群将最终绝灭;在原系统只有一个全局稳定的边界平衡点时,反馈控制变量仅改变正平衡点的位置,而不会改变边界平衡点的稳定性.     

Ivlev型捕食系统的全局动力学分析

研究捕食者与食饵均具有线性密度制约的Ivlev型捕食动力系统.应用常微分方程定性方法,得到了正平衡点的全局稳定性和非小振幅极限环的存在唯一性的充分条件.特别地,在一定条件下,证明了极限环的存在唯一性与正平衡点的局部不稳定性是等价的,正平衡点的局部稳定性隐含它的全局稳定性,因此,系统的全局动力学性质完全由正平衡点的局部性质所决定.     

具有时滞的单种群扩散模型的全局稳定性

该文研究了一类具有时滞的单种群扩散模型, 利用同伦技术得到了模型存在正平衡点. 在适当的条件下证明了系统是一致持续的, 获得了系统的正平衡点的局部和全局稳定性的充分条件.     

基于比率的广义Holling-Tanner系统的全局渐近稳定性

本文对基于比率的广义Holling-Tanner系统进行了定性分析,给出了系统解有界的条件和平衡点局部稳定的条件．通过构造适当的Liapunov函数,得到了正平衡点全局渐近稳定性的充分条件．     

The limit cycles of a second-order system of differential equations: The method of small forms

In this paper we investigate the existence of limit cycles of a system of the second-order differential equations with a vector parameter.We propose a method for representing a solution as a sum of forms with respect to the initial value and the parameter; we call this technique the method of small forms. We establish the conditions under which a sufficiently small neighborhood of the equilibrium point contains no limit cycles. We construct a polynomial, whose positive roots of odd multiplicity define the lower bound for the number of cycles, and simple positive roots (other positive roots do not exist) define the number of limit cycles in a sufficiently small neighborhood of the equilibrium point.We prove theorems, whose conditions guarantee that a positive root of odd multiplicity defines a unique limit cycle, but a positive root of even multiplicity defines exactly two limit cycles.We propose a method for defining the type of the stability of limit cycles.     

Stability of equilibrium points of demand-inventory model with stock-dependent demand

A model of demand and inventory of a product in one echelon of supply chain is considered. The model is formulated as a system of difference equations, in which every equilibrium point is nonhyperbolic. A positive invariant set of the system is constructed. An analysis of properties of equilibrium points of the system is based on the Lyapunov method or reducing it to the family of systems of difference equations with hyperbolic equilibrium points.     

一类时滞分数阶计算机病毒模型的稳定性研究

本文研究一类改进的时滞分数阶计算机病毒模型正平衡点的稳定性问题.利用线性化方法和拉普拉斯变换获得模型对应的线性化系统的特征方程,通过讨论特征方程的根以及横截条件研究时滞和正平衡点稳定性之间的关系,推导了Hopf分支出现时时滞临界值的计算公式,并选择恰当的系统参数进行数值模拟以验证理论分析的合理性.     

Analysis of Dynamic Properties of Forest Beetle Outbreak Model

This paper mainly studies the dynamic properties of the forest beetle outbreak model. The existence of the positive equilibrium point and the local stability of the positive equilibrium point of the system are analyzed, and the relevant conclusions are drawn. After that, the existence of Turing instability, Hopf bifurcation and Turing-Hopf bifurcation are discussed respectively, and the necessary conditions for existence are given. Finally, the normal form of the Turing-Hopf point is calculated, and some dynamic properties at the point are analyzed by numerical simulation.     

一类三次Kolmogorov系统的极限环分支

本文研究了一类三次Kolmogorov系统，得出了该系统可分支出三个极限环，且其中有两个是稳定的，同时给出了其中心条件.     

Global dynamics of a competitive system of rational difference equations

In this paper, we study the qualitative behavior of a competitive system of second‐order rational difference equations. More precisely, we investigate the boundedness character, existence and uniqueness of positive equilibrium point, local asymptotic stability and global stability of the unique positive equilibrium point and rate of convergence of positive solutions of the system. Some numerical examples are given to verify our theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Oscillation and attractivity of discrete nonlinear delay population model

In this paper, we consider the discrete nonlinear delay model which describe the control of a single population of cells. We establish a sufficient condition for oscillation of all positive solutions about the positive equilibrium point and give a sufficient condition for the global attractivity of the equilibrium point. The oscillation condition guarantees the prevalence of the population about the positive steady sate and the global attractivity condition guarantees the nonexistence of dynamical diseases on the population.     

Global qualitative analysis of a discrete host‐parasitoid model with refuge and strong Allee effects

In this paper, we discuss the qualitative behavior of a discrete host‐parasitoid model with the host subject to refuge and strong Allee effects. More precisely, we study the local and global asymptotic stability, stable manifolds and unstable manifolds of boundary equilibrium points, existence and unique positive equilibrium point, local and global behavior of the positive equilibrium point, and the uniform persistence for the model with the host subject to the refuge or both refuge and strong Allee effects. It is also proved that the model undergoes a transcritical bifurcation in a small neighborhood of the boundary equilibrium point. Some numerical simulations are given to support our theoretical results. We can obtain that the addition of the refuge may make the parasitoids go extinct while the hosts survive or may stabilize the host‐parasitoid interaction; the addition of both refuge and strong Allee effects has either a negative or positive impact on the coexistence of both populations.     

Global bifurcation of positive equilibria in nonlinear population models

Existence of nontrivial nonnegative equilibrium solutions for age-structured population models with nonlinear diffusion is investigated. Introducing a parameter measuring the intensity of the fertility, global bifurcation is shown of a branch of positive equilibrium solutions emanating from the trivial equilibrium. Moreover, for the parameter-independent model we establish existence of positive equilibria by means of a fixed point theorem for conical shells.     

一类具有Watt型功能性反应的捕食系统的极限环与稳定性

研究一类具有Watt型功能性反应的捕食模型.讨论了该系统正平衡点的存在性以及非负平衡点的性态,应用Poincare-Bendixson定理和张芷芬定理,证明了极限环的存在性和唯一性,并采用构造Dulac函数的方法,获得了正平衡点全局渐近稳定性的一个充分条件.