三种群L0tka-V0lterra周期系数混合模型的全局渐近稳定性

本文考虑周期系数的三种群Lokta-Volterra模型,种群间既有捕食关系又有竞争关系,得到其正周期解的存在性及其全局渐近稳定性的条件,且举例说明条件的可行性.     

周期系数三种群Lotka－Volterra混合模型分析

考虑三种群Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ周期系数模型，种群间既有捕食关系又有竞争关系，得到唯一存在全局渐近稳定周期解的条件，并举例说明条件的可行性．     

周期系数三种群Lotka—Volterra混合模型分析

考虑三种群Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ周期系数模型，种群间既有捕食关系又有竞争关系，得到唯一存在全局渐近稳定周期解的条件，并举例文明条件的可行性。     

五种群Lotka-Volterra混合系统的全局渐近稳定性

考虑周期系数的五种群Lotka-Volterra模型,种群间既有捕食关系又有竞争关系,得到该系统的正周期解的存在性及全局渐近稳定性的条件.     

带有时滞的非自治三种群Lotka-volterra混合模型的渐近性

讨论非自治的周期系数的Lotka-volterra三种群时滞混合摸型,种群间既有捕食关系又有竞争关系,当系数满足一定条件时模型的持久性,进而获得了模型正周期解存在与全局渐近稳定的充分条件,并举例说明条件的可行性.     

具周期输入的有限连续分布时滞神经网络周期解的全局指数稳定性

在去掉对激励函数有界、连续可导、平均时滞有界的条件下,仅要求激励函数满足Lip-schitz条件和连接权矩阵之间的关系是一个M-矩阵的情形下,利用重合度理论、Dini导数等知识得出了具周期输入的有限连续分布的一类细胞神经网络周期解的存在性.利用Dini导数和不等式分析技术在同样条件下得出了周期解的指数稳定性.推广和改进了前人的结论.并举例说明了所得定理的有效性.     

拓扑Markov链——非游荡集和拓扑熵

本文讨论了拓扑Markov链,给出了涉及拓扑熵、紊动点偶、ω-极限集、非游荡集、周期点集和终于周期点集之间关系的7个等价条件。     

一类具有逐段常变量神经网络系统概周期解存在性与指数稳定性

利用Halanay不等式,我们得到了一类具有逐段常变量神经网络系统解全局指数稳定的一个充分条件;此外,在同样条件下,通过不动点定理,证明了这类概周期系统概周期解的存在唯一性与模包含关系．     

一阶多智能体系统的一致性分析

研究一阶连续多智能体系统的一致性问题,其中每个智能体只能在一系列离散时刻上获得其相对邻居的状态信息,并且每个智能体的保持器的周期和采样器的周期是不同的.通过分析多智能体系统的稳定性,获得了一致性成立的充要条件,该条件揭示了交流拓扑、控制器增益、采样器的周期和保持器的周期的关系.最后,提供一个仿真例子以说明理论结果的有效性.     

具有Holling功能反应的非自治捕食系统的持续性和周期解

研究了具有一般的Holling功能反应函数,且种群之间既有捕食关系,又有竞争关系的三种群混合模型,得到了该系统惟一存在全局渐近稳定正周期解的条件,推广了已有结论.     

Stability in a diffusive food-chain model with Michaelis–Menten functional response

This paper deals with the behavior of positive solutions to a reaction–diffusion system with homogeneous Neumann boundary conditions describing a three species food chain. A sufficient condition for the local asymptotical stability is given by linearization and also a sufficient condition for the global asymptotical stability is given by a Lyapunov function. Our result shows that the equilibrium solution is globally asymptotically stable if the net birth rate of the first species is big enough and the net death rate of the third species is neither too big nor too small.     

三种群食饵系统的概周期解

本文研究了一类三种群概周期食饵系统 ,并给出了其存在唯一的全局渐近稳定的正概周期解的充分条件。     

一类具有Ⅲ 类功能反应的三维顺环捕食系统的研究(英文)

研究一类具有 类功能反应的三维顺环捕食系统 ,得到了该系统持久性 ,周期解的存在性及全局渐近稳定性的充分条件 .     

具有时滞的三个混合种群模型的周期解

利用重合度理论中连续性定理 ,得到了三种群时滞混合模型正周期解存在性的判别准则     

Food chain model with optimal harvesting in fuzzy environment

A multispecies harvesting model with mutual interactions is formulated based on Lotka–Voltera model with three competing species which are affected not only by harvesting but also by the presence of prey, predator and the third species, which is super predator. In order to understand the dynamics of the system, it is assumed that the super predator follows the logistic growth. Further, there is demand for all the above three species in the market and hence harvesting of all species is performed. We derive the condition for global stability of the system using a suitable Lyapunov function. The possibility of existence of bioeconomic equilibrium is discussed. The optimal harvest policy is studied and the solution is derived under imprecise inflation in fuzzy environment using Pontryagin’s maximal principle. Finally some numerical examples are discussed to illustrate the model.     

三种群食物链交错扩散模型的整体

本文应用能量估计方法和Gagliardo-Nirenberg型不等式证明了一类强耦合反应扩散系统整体解的存在性和一致有界性，该系统是带自扩散和交错扩散项的三种群Lotka-Volterra食物链模型．通过构造Lyapunov函数给出了该模型正平衡点全局渐近稳定的充分条件．     

具有脉冲效应的三种群食物链系统正周期解的存在性

利用重合度理论中的连续定理,研究了一类在周期环境中具有脉冲效应的三种群食物链系统,得到了其正周期解存在的充分条件.     

Numerical solutions for some coupled systems of nonlinear boundary value problems

Summary In the well-known Volterra-Lotka model concerning two competing species with diffusion, the densities of the species are governed by a coupled system of reaction diffusion equations. The aim of this paper is to present an iterative scheme for the steady state solutions of a finite difference system which corresponds to the coupled nonlinear boundary value problems. This iterative scheme is based on the method of upper-lower solutions which leads to two monotone sequences from some uncoupled linear systems. It is shown that each of the two sequences converges to a nontrivial solution of the discrete equations. The model under consideration may have one, two or three nonzero solutions and each of these solutions can be computed by a suitable choice of initial iteration. Numerical results are given for these solutions under both the Dirichlet boundary condition and the mixed type boundary condition.     

Global asymptotic stability of positive equilibrium of three-species Lotka–Volterra mutualism models with diffusion and delay effects

In the mutualism system with three species if the effects of dispersion and time delays are both taken into consideration, then the densities of the cooperating species are governed by a coupled system of reaction–diffusion equations with time delays. The aim of this paper is to investigate the asymptotic behavior of the time-dependent solution in relation to a positive uniform solution of the corresponding steady-state problem in a bounded domain with Neumann boundary condition, including the existence and uniqueness of a positive steady-state solution. A simple and easily verifiable condition is given to ensure the global asymptotic stability of the positive steady-state solution. This result leads to the permanence of the mutualism system, the instability of the trivial and all forms of semitrivial solutions, and the nonexistence of nonuniform steady-state solution. The condition for the global asymptotic stability is independent of diffusion and time-delays as well as the net birth rate of species, and the conclusions for the reaction–diffusion system are directly applicable to the corresponding ordinary differential system and 2-species cooperating reaction–diffusion systems. Our approach to the problem is based on inequality skill and the method of upper and lower solutions for a more general reaction–diffusion system. Finally, the numerical simulation is given to illustrate our results.     

Existence of optimal solution and optimality condition for parameter identification of an ecological species system

Parameter identification problem of a three species (predator, mutualist-prey, and mutualist) ecological system with reaction-diffusion phenomenon is investigated in this paper. The mathematical model of the parameter identification problem is constructed and continuous dependence of the solution for the direct problem on the parameters identified is obtained. Finally, the existence of optimal solution and an optimality necessary condition for the parameter identification problem are given.