一类食物链模型的全局定性分析

文系统地研究了由一个食饵种群和两个捕食者种群所构成的食物链系统.结论表明：种群间的相互作用可以导致两个捕食者种群灭绝或一个捕食者种群灭绝,或者所有三个种群能以稳定的正平衡态或振动解的形式共存.利用MATLAB软件,该文提供了两个例子来模拟这些结论.     

具有时滞和Ivlev功能反应的食物链模型的研究

建立了一个具有时滞和Ivlev功能性反应的食物链模型.同时选择了一个分支参数τ,分析了发生Hopf分支的情况,得出了Hopf分支发生的条件,并用数值模拟验证了分析结果.     

一类时滞造血模型的全局Hopf分支

对一类具有时滞的造血模型,通过讨论线性部分超越特征方程根的分布情况,得到了正平衡点的稳定性及局部Hopf分支的存在性.进而利用吴建宏建立的全局分支理论,将周期解的存在性由局部延拓到全局.     

具有时滞的食物链系统的Hopf分支

本文研究了具有时滞的三种群食物链模型的分支问题.利用分支理论及Nyquist准则等方法,获得了系统永久持续生存和正平衡点附近发生Hopf分支的条件.文中进一步研究得到了系统保持稳定的最大时滞长度,从而可以了解并控制种群密度发生异常振荡,推广了已有文献的结果.     

具有Monod-Haldane功能反应和脉冲效应的捕食系统的动力学性质

基于综合害虫防治,对具脉冲效应的Monod—Haldane功能反应的捕食系统进行了分析,根据Floquet乘子理论,获得了害虫灭绝周期解全局渐近稳定与系统持续生存的条件．并讨论了害虫灭绝周期解附近分支出非平凡周期解的问题,且文章利用Matlab软件对害虫灭绝周期解害虫周期爆发现象进行了数值模拟．     

具有扩散和群体防卫的简单食物链的Hopf分支

具有扩散和群体防卫的简单食物链的Ｈｏｐｆ分支李云（武汉水运工程学院基础部，武汉４３００６３）ＴＨＥＨＯＰＦＢＩＦＵＲＣＡＴＩＯＮＦＯＲＳＩＭＰＬＥＦＯＯＤＣＨＡＩＮＷＩＴＨＤＩＦＦＵＳＩＯＮＡＮＤＧＲＯＵＰＤＥＦＥＮＣＥ￥ＬＩＹＵＮ（Ｄｅｐａｒｔｍｅ...     

带有Leslie-Gower功能性反应的三维食物链模型研究

研究了离散时间上带有Leslie-Gower功能性反应的三维食物链模型.首先给出保证系统永久持续生成的条件,由于系统系数的周期性,正周期解是存在的,最后通过在正的周期解领域内线性化系统,并通过构造Lyapunov函数,我们得出了保证系统正周期解全局稳定的条件.     

具有时滞的Goodwin增长周期模型

本文将离散时滞引入 Goodwin增长周期模型中 ,借助于 Hopf分支定理 ,得到了周期解的存在性 ,发展了 Lorenz,Chiarella等学者关于 Goodwin模型经济周期方面的研究结果     

Gause型食物链模型Hopf分支的存在性分析

考虑了一类三维时滞Gause型食物链模型.首先分析了共存平衡点稳定的条件,然后利用多项式理论分析了特征方程特征根的分布,得到了Hopf分支存在的条件,最后给出了几组数值模拟验证文中得到的结论,进一步预测了Hopf分支的全局存在性.     

一类具有时滞的商业周期模型的分支控制

应用一种基于时滞反馈的分支控制方法,对一类具有时滞的商业周期模型的Hopf分支进行了控制.以时滞作为分支参数,当时滞达到某个阈值时,无控系统失去稳定性,Hopf分支产生:将时滞反馈控制器引入无控系统,可以使Hopf分支延迟发生或消失.数值仿真的结果验证了该方法的有效性.     

Analysis of the Dynamics of a Predator-prey Model with Holling Functional Response

A diffusive predator-prey system with Holling functional response is considered. Firstly, existence of positive equilibrium of this reaction diffusion model under Neumann boundary condition is obtained. Meanwhile, the existence conditions for Turing instability and Hopf bifurcations of a system with Holling \uppercase\expandafter{\romannumeral2} functional response are established. Next, the existence of the hydra effect is demonstrated, when the system is undergoing non-homogeneous steady-state solutions. Finally, numerical simulations are illustrated to support our theory results.     

Dynamics analysis of a delayed viral infection model with immune impairment

In this paper, the dynamical behavior of a delayed viral infection model with immune impairment is studied. It is shown that if the basic reproductive number of the virus is less than one, then the uninfected equilibrium is globally asymptotically stable for both ODE and DDE model. And the effect of time delay on stabilities of the equilibria of the DDE model has been studied. By theoretical analysis and numerical simulations, we show that the immune impairment rate has no effect on the stability of the ODE model, while it has a dramatic effect on the infected equilibrium of the DDE model.     

具有时滞的生态流行病模型的稳定性和Hopf分支

该文考虑一类食饵染病的时滞捕食被捕食模型. 作者分析了系统的非负不变性, 边界平衡点的性质和全局稳定性. 证明了当时滞τ=τ\-1+τ\-2适当小时, 正平衡点是局部渐近稳定的,随着时滞的增加, 正平衡点由稳定变为不稳定, 系统在正平衡点附近发生Hopf分支.     

具有多时滞的食物链系统的Hopf分支

讨论了具有时滞的食物链模型,首先我们得到了系统永久持续生存的条件,然后讨论系统在正平衡点附近发生Hopf分支的存在性;最后利用数值模拟证明所得结论.     

Analysis of Dynamics in a Complex Food Chain with Ratio-Dependent Functional Response

In this paper, we study a new model obtained as an extension of athree-species food chain model with ratio-dependent functional response. We provide non-persistence and permanence results and investigate the stability of all possible equilibria in relation tothe ecological parameters. Results are obtained for the trivial andprey-only equilibria where the singularity of the model prevents linearization, and the remaining semi-trivial equilibria are studiedusing linearization. We provide a detailed analysis of conditionsfor existence, uniqueness, and multiplicity of coexistencee quilibria, as well as permanent effect for all species. The complexity of the dynamics in this model is theoretically discussedand graphically demonstrated through various examples and numerical simulations.     

Dynamics of an intraguild predation food web model with strong Allee effect in the basal prey

Since intraguild predation (IGP) is a ubiquitous and important community module in nature and Allee effect has strong impact on population dynamics, in this paper we propose a three-species IGP food web model consisted of the IG predator, IG prey and basal prey, in which the basal prey follows a logistic growth with strong Allee effect. We investigate the local and global dynamics of the model with emphasis on the impact of strong Allee effect. First, positivity and boundedness of solutions are studied. Then existence and stability of the boundary and interior equilibria are presented and the Hopf bifurcation curve at an interior equilibrium is given. The existence of a Hopf bifurcation curve indicates that if competition between the IG prey and IG predator for the basal resource lies below the curve then the interior equilibrium remains stable, while if it lies above the curve then the interior equilibrium loses its stability. In order to explore the impact of Allee effect, the parameter space is classified into sixteen different regions and, in each region, the number of interior equilibria is determined and the corresponding bifurcation diagrams on the Allee threshold are given. The extinction parameter regions of at least one species and the necessary coexistence parameter regions of all three species are provided. In addition, we explore possible dynamical patterns, i.e., the existence of multiple attractors. By theoretical analysis and numerical simulations, we show that the model can have one (i.e. extinction of all species), two (i.e. bi-stability) or three (i.e. tri-stability) attractors. It is also found by simulations that when there exists a unique stable interior equilibrium, the model may generate multiple attracting periodic orbits and the coexistence of all three species is enhanced as the competition between the IG prey and IG predator for the basal resource is close to the Hopf bifurcation curve from below. Our results indicate that the intraguild predation food web model exhibits rich and complex dynamic behaviors and strong Allee effect in the basal prey increases the extinction risk of not only the basal prey but also the IG prey or/and IG predator.     

Dynamics of an epidemic model with relapse and delay

In this paper, we consider a new epidemiological model with delay and relapse phenomena. Firstly, a basic reproduction number $R_0$ is identified, which serves as a threshold parameter for the stability of the equilibria of the model. Then, beginning with the delay-free model, the global asymptotic stability of the equilibria is obtained through the construction of suitable Lyapunov functions. For the delay model, the stability of the positive equilibrium and the existence of the local Hopf bifurcation are discussed. Furthermore, the application of the normal form theory and center manifold theorem is used to determine the direction and stability of these Hopf bifurcations. Finally, we shed light on corresponding biological implications from a numerical perspective. It turns out that time delay affects the stability of the positive equilibrium, leading to the occurrence of periodic oscillations and disease recurrence.     

Dynamics of a Delayed Predator-prey System with Stage Structure for Predator and Prey

In this paper, a predator-prey system with two discrete delays and stage structure for both the predator and the prey is investigated. The dynamical behaviors such as local stability and local Hopf bifurcation are analyzed by regarding the possible combinations of the two delays as bifurcating parameter. Some explicit formulae determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form method and the center manifold theory. Finally, numerical simulations are presented to support the theoretical analysis.     

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.