一类具有时滞的捕食模型的稳定性和Hopf分支

研究一类具有时滞和Beddington-DeAngelis功能性反应的捕食模型的稳定性和Hopf分支.以滞量为参数,得到了系统正平衡点的稳定性和Hopf分支存在的充分条件.应用一般泛函微分方程的度理论,研究了该系统的全局Hopf分支的存在性.     

一类具有阶段结构和时滞的捕食模型的稳定性及Hopf分支(英文)

研究一类具有阶段结构和时滞的捕食模型.通过特征方程分别分析了正平衡点和边界平衡点的局部稳定性,到了系统Hopf分支存在的充分条件.通过规范型理论和中心流型定理,给出了确定Hopf分支方向和分支周期解的稳定性的计算公式.     

一类具有时滞和Holling Ⅲ型功能性反应的捕食模型的稳定性和Hopf分支

研究一类具有时滞和Holling Ⅲ型功能性反应的捕食模型的稳定性和Hopf分支.以滞量为参数,得到了系统正平衡点的稳定性和Hopf分支存在的充分条件,给出了确定Hopf分支方向和分支周期解的稳定性的计算公式.     

具离散和连续时滞的三阶段结构捕食系统的Hopf分支

研究了一类具离散和连续时滞作用的三阶段结构捕食系统,分析了系统平衡点的存在性和稳定性,得到了系统发生局部Hopf分支的充分条件,并给出了相应的数值例子和结论.     

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.     

一类具时滞的生理模型的Hopf分支

本文研究了一类简化的具时滞的生理模型的稳定性和Ｈｏｐｆ分支．首先,以滞量为参数,应用Ｃｏｏｋｅ的方法,把Ｒ＾＋分为两个区间,使当滞量属于相应区间时,所考虑的模型的平凡解是稳定或不稳定的,同时得到了Ｈｏｐｆ分支值．然后,应用中心流形和规范型理论,得到了关于确定Ｈｏｐｆ分支方向和分支周期解的稳定性的计算公式．最后,应用Ｍａｔｈｅｍａｔｉｃａ软件进行了数值模拟。     

时滞湖泊生态模型的稳定性与Hopf分支

研究了具有时滞的外来有机物-浮游植物-浮游动物湖泊生态模型.通过研究该模型在平衡点处的特征方程,得到了使平衡点稳定的时滞的取值范围.并且发现当时滞取某些特定值时,在平衡点附近会出现周期解.与已有的研究结果相比较发现,时滞对湖泊生态系统的稳定性有着重要的影响.最后,我们给出一个数值算例来验证理论结果.     

一类具有时滞Holling-Ⅲ型捕食-食饵系统的Hopf分支

研究了具有时滞的Holling-Ⅲ型捕食-食饵系统,其中捕食者的数量反应具有leslies形式.采用常微分定性与稳定性方法,推出了当τ=0时,正平衡点全局稳定性的充分条件,并考虑了时滞对于模型稳定性的影响,选取时滞τ作为分支参数,得出了在正平衡点附近产生Hopf分支.     

一类带无选择性捕获和时滞的捕食食饵系统的Hopf分支分析

本文主要研究了一个改进的带时滞和无选择捕获函数的捕食-食饵生态经济系统的稳定性和Hopf分支.利用微分代数系统的稳定性理论和分支理论,得到了系统正平衡点稳定性的条件,以及当时滞τ作为分支参数时系统产生Hopf分支的条件.对Leslie-Gower捕食-食饵模型进行了一定程度的完善,使得建立的模型更符合实际情况,因此得到的结论也更加科学.     

具有时滞结构工人再培训模型的稳定性及Hopf分支

通过分析特征方程及Hurwitz判定定理,讨论了系统正平衡点存在局部渐近稳定的充分条件及正平衡点附近存在Hopf分支的充分条件;进一步利用中心流形定理和规范型理论给出了Hopf分支的分支方向及分支周期解的稳定性.最后通过选取适当的参数和不同的时滞值对该系统进行Matlab数值模拟,得到系统在临界值附近的各分量变化图和解曲线走势图.结果表明,随着分支参数值的变化,系统的稳定性会发生变化,同时系统也会产生Hopf分支.     

A stage-structured predator-prey system with time delay

A stage-structured predator-prey system with time delay is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated. The existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results. Based on the global Hopf bifurcation theorem for general functional differential equations, the global existence of periodic solutions is established.     

Hopf bifurcation in a environmental defensive expenditures model with time delay

In this paper a three-dimensional environmental defensive expenditures model with delay is considered. The model is based on the interactions among visitors V, quality of ecosystem goods E, and capital K, intended as accommodation and entertainment facilities, in Protected Areas (PAs). The tourism user fees (TUFs) are used partly as a defensive expenditure and partly to increase the capital stock. The stability and existence of Hopf bifurcation are investigated. It is that stability switches and Hopf bifurcation occurs when the delay t passes through a sequence of critical values, τ₀. It has been that the introduction of a delay is a destabilizing process, in the sense that increasing the delay could cause the bio-economics to fluctuate. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation are exhibited by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the results.     

Hopf bifurcation analysis of a predator-prey system with Holling type IV functional response and time delay

This paper is concerned with a predator-prey system with Holling type IV functional response and time delay. Our aim is to investigate how the time delay affects the dynamics of the predator-prey system. By choosing the delay as a bifurcation parameter, the local asymptotic stability of the positive equilibrium and existence of local Hopf bifurcations are analyzed. Based on the normal form and the center manifold theory, the formulaes for determining the properties of Hopf bifurcation of the predator-prey system are derived. Finally, to support these theoretical results, some numerical simulations are given to illustrate the results.     

Global stability and Hopf bifurcation of a plankton model with time delay

A differential delay equation model with a discrete time delay and a distributed time delay is introduced to simulate zooplankton–nutrient interaction. The differential inequalities’ methods and standard Hopf bifurcation analysis are applied. Some sufficient conditions are obtained for persistence and for the global stability of the unique positive steady state, respectively. It was shown that there is a Hopf bifurcation in the model by using the discrete time delay as a bifurcation parameter.     

The asymptotic behaviors of a stage-structured autonomous predator-prey system with time delay

In this paper, we consider an autonomous predator-prey Lotka-Volterra system in which individuals in the population may belong to one of two classes: the immatures and the matures, the age to maturity is represented by a time delay. By using eigenvalue analysis, principal term analyze method, reduction to absurdity, and iterative method, we obtain some simple conditions for global asymptotic stability of the unique positive equilibrium point. Moreover, a condition that the prey population in the system get extinction and the predator population in the system get permanence will be obtained. Meanwhile the theorems extend the corresponding conclusions in which there have no two stage structures.     

Stability and Hopf bifurcation analysis of a predator-prey model with time delayed incomplete trophic transfer

A new nonlinear predator-prey model with incomplete trophic transfer is introduced. In this model,we assume that the rate of the trophic absorption of the predator is less than the rate of the conversion of consumed prey to predator in the Ivlev-type functional responses. The existence and uniqueness of the positive equilibrium of the model and the stability of the equilibrium of the model are studied under various conditions.Hopf bifurcation analysis of the delayed model is provided.     

Hopf bifurcation analysis in a tri-neuron network with time delay

A neural network model with three neurons and a single delay is considered. The existence of local Hopf bifurcations is first considered and then explicit formulas are derived by using the normal form method and center manifold theory to determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. A global Hopf bifurcation theorem due to Wu and a Bendixson's criterion for high-dimensional ODE due to Li and Muldowney are used to obtain a group of conditions for the system to have multiple periodic solutions when the delay is sufficiently large. Finally, numerical simulations are carried out to support the theoretical analysis of the research.     

Properties of stability and Hopf bifurcation for a HIV infection model with time delay

In this paper, we consider the classical mathematical model with saturation response of the infection rate and time delay. By stability analysis we obtain sufficient conditions for the global stability of the infection-free steady state and the permanence of the infected steady state. Numerical simulations are carried out to explain the mathematical conclusions.     

Hopf bifurcation analysis of a food-limited population model with delay

The dynamics of a food-limited population model with delay are investigated. We prove that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. An explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived, using the theory of normal form and center manifold. Global existence of periodic solutions is established by using a global Hopf bifurcation result due to [J. Wu, Symmetric functional differential equations and neural networks with memory, Trans. Amer. Math. Soc. 350 (1998) 4799–4838].     

Hopf bifurcation in a two-competitor, one-prey system with time delay

In this paper, we consider a delayed two-competitor/one-prey system in which both two competitors exhibit Holling II functional response. By choosing the time delay as a bifurcation parameter, it is found that the Hopf bifurcation occurs when the delay passes through a certain critical value. Numerical simulations are performed to illustrate the analytical results.