多时滞合作系统的稳定性与全局Hopf分支

以时滞为参数,研究了一类多时滞合作系统的正平衡点的稳定性及局部Hopf分支的存在性.在此基础上结合一般泛函微分方程的全局Hopf分支定理,讨论了该系统全局Hopf分支的存在性.     

具有群体效应和时滞的交叉扩散捕食-食饵系统的Hopf分支（英文）

本文研究具有群体效应和时滞的交叉扩散捕食-食饵模型的Hopf分支.将死亡率β和时滞τ作为分支因子,通过分析特征方程,讨论系统正平衡点E_3(u~*,v~*)的稳定性和Hopf分支的存在性.我们得到当参数值穿过临界值时,该系统会在正平衡点E_3附近产生Hopf分支.最后,我们进行数值模拟,验证了结论的正确性.     

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.     

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.     

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.     

Degn-Harrison反应扩散系统的Turing不稳定性与Hopf分支

在齐次Neumann边界条件下研究一类Degn-Harrison反应扩散系统.首先讨论常微分系统正平衡点的稳定性和Hopf分支,其次研究扩散系统,给出扩散系数对正平衡点稳定性的影响,建立系统的Turing不稳定性,同时在扩散系数满足一定条件时给出Hopf分支的存在性.     

多时滞捕食-食饵系统正平衡点的稳定性及全局Hopf分支

本文首先用Cooke等人建立的关于超越函数的零点分布定理,研究了一类多时滞捕食-食饵系统正平衡点的稳定性及局部Hopf分支,在此基础上再结合吴建宏等人用等变拓扑度理论建立起的一般泛函微分方程的全局Hopf分支定理,进一步研究了该系统的全局Hopf分支.     

多时滞捕食-食饵系统正平衡点的稳定性及全局Hopf分支

本文首先用Cooke等人建立的关于超越函数的零点分布定理,研究了一类多时滞捕食-食饵系统正平衡点的稳定性及局部Hopf分支,在此基础上再结合吴建宏等人用等变拓扑度理论建立起的一般泛函微分方程的全局Hopf分支定理,进一步研究了该系统的全局Hopf分支.     

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.     

Bifurcation of a Modified Leslie-Gower System with Discrete and Distributed Del

A modified Leslie-Gower predator-prey system with discrete and distributed delays is introduced. By analyzing the associated characteristic equation, stability and local Hopf bifurcation of the model are studied. It is found that the positive equilibrium is asymptotically stable when $\tau$ is less than a critical value and unstable when $\tau$ is greater than this critical value and the system can also undergo Hopf bifurcation at the positive equilibrium when $\tau$ crosses this critical value. Furthermore, using the normal form theory and center manifold theorem, the formulae for determining the direction of periodic solutions bifurcating from positive equilibrium are derived. Some numerical simulations are also carried out to illustrate our results.     

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.     

Hopf bifurcations in a predator–prey system with a discrete delay and a distributed delay

A delayed Lotka–Volterra two-species predator–prey system with discrete hunting delay and distributed maturation delay for the predator population described by an integral with a strong delay kernel is considered. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations are demonstrated. It is found that under suitable conditions on the parameters the positive equilibrium is asymptotically stable when the hunting delay is less than a certain critical value and unstable when the hunting delay is greater than this critical value. Meanwhile, according to the Hopf bifurcation theorem for functional differential equations (FDEs), we find that the system can also undergo a Hopf bifurcation of nonconstant periodic solution at the positive equilibrium when the hunting delay crosses through a sequence of critical values. In particular, by applying the normal form theory and the center manifold reduction for FDEs, an explicit algorithm determining the direction of Hopf bifurcations and the stability of bifurcating periodic solutions occurring through Hopf bifurcations is given. Finally, to verify our theoretical predictions, some numerical simulations are also included at the end of this paper.     

Bifurcation analysis of a modified Holling-Tanner predator-prey model with time delay

In this paper, a modified Holling-Tanner predator-prey model with time delay is considered. By regarding the delay as the bifurcation parameter, the local asymptotic stability of the positive equilibrium is investigated. Meanwhile, we find that the system can also undergo a Hopf bifurcation of nonconstant periodic solution at the positive equilibrium when the delay crosses through a sequence of critical values. In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions, an explicit algorithm is given by applying the normal form theory and the center manifold reduction for functional differential equations. Finally, numerical simulations supporting the theoretical analysis are also included.     

时滞偏害系统的稳定性和分歧分析

本文讨论了具离散和分布时滞的偏害系统.以时滞作为分歧参数,通过分析原系统在正平衡点处线性化系统的特征方程,获得了正平衡点渐近稳定以及在它周围分歧出周期解的条件.另外,通过使用规范形和中心流形定理,我们获得了Hopf分歧的方向和分歧周期解稳定性的显式算法.最后,数值模拟支持了我们的理论分析.     

Chaos and Hopf bifurcation analysis for a two species predator–prey system with prey refuge and diffusion

In this paper, a delayed predator–prey model with Holling type II functional response incorporating a constant prey refuge and diffusion is considered. By analyzing the characteristic equation of linearized system corresponding to the model, we study the local asymptotic stability of the positive equilibrium of the system. By choosing the time delay due to gestation as a bifurcation parameter, the existence of Hopf bifurcations at the positive equilibrium is established. By applying the normal form and the center manifold theory, an explicit algorithm to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Further, an example is presented to illustrate our main results. Finally, recurring to the numerical method, the influences of impulsive perturbations on the dynamics of the system are also investigated.     

Dynamics of a competitive Lotka-Volterra system with three delays

In this paper, a competitive Lotka-Volterra system with three delays is investigated. By choosing the sum τ of three delays as a bifurcation parameter, we show that in the above system, Hopf bifurcation at the positive equilibrium can occur as τ crosses some critical values. And we obtain the formulae determining direction of Hopf bifurcation and stability of the bifurcating periodic solutions by using the normal form theory and center manifold theorem. Finally, numerical simulations supporting our theoretical results are also included.     

具有捕食者相互残杀项时滞系统的Hopf分支

研究了具有捕食者相互残杀项的时滞系统的Hopf分支,通过选择时滞作为一个分支参数,研究了正平衡点的稳定性和正周期解的Hopf分支.而且通过应用规范型和中心流形的理论,得出了确定分支方向的明确的算法.     

Bifurcation of an eco-epidemiological model with a nonlinear incidence rate

A predator-prey system with disease in the prey is considered. Assume that the incidence rate is nonlinear, we analyse the boundedness of solutions and local stability of equilibria, by using bifurcation methods and techniques, we study Bogdanov-Takens bifurcation near a boundary equilibrium, and obtain a saddle-node bifurcation curve, a Hopf bifurcation curve and a homoclinic bifurcation curve. The Hopf bifurcation and generalized Hopf bifurcation near the positive equilibrium is analyzed, one or two limit cycles is also discussed.