共查询到16条相似文献,搜索用时 109 毫秒
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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. 相似文献
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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. 相似文献
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一类具有时滞Holling-Ⅲ型捕食-食饵系统的Hopf分支 总被引:1,自引:0,他引:1
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. 相似文献
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多时滞捕食-食饵系统正平衡点的稳定性及全局Hopf分支 总被引:1,自引:0,他引:1
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. 相似文献
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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. 相似文献
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A kind of three species delayed predator-prey system with reserve area for prey and in the presence of toxicity is proposed in this paper.Local stability of the coexistence equilibrium of the system and the existence of a Hopf bifurcation is established by choosing the time delay as the bifurcation parameter.Explicit formulas to determine the direction and stability of the Hopf bifurcation are obtained by means of the normal form theory and the center manifold theorem.Finally,we give a numerical example to illustrate the obtained results. 相似文献
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Stability and Hopf bifurcation of a delayed predator-prey system with nonlocal competition and herd behaviour 下载免费PDF全文
In this paper, we investigate the stability and Hopf bifurcation of a diffusive predator-prey system with herd behaviour. The model is described by introducing both time delay and nonlocal prey intraspecific competition. Compared to the model without time delay, or without nonlocal competition, thanks to the together action of time delay and nonlocal competition, we prove that the first critical value of Hopf bifurcation may be homogenous or non-homogeneous. We also show that a double-Hopf bifurcation occurs at the intersection point of the homogenous and non-homogeneous Hopf bifurcation curves. Furthermore, by the computation of normal forms for the system near equilibria, we investigate the stability and direction of Hopf bifurcation. Numerical simulations also show that the spatially homogeneous and non-homogeneous periodic patters. 相似文献
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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. 相似文献
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Spatiotemporal dynamics in a predator-prey model with a functional response increasing in both predator and prey densities 下载免费PDF全文
In this paper, we studied a diffusive predator-prey model with a functional response increasing in both predator and prey densities. The Turing instability and local stability are studied by analyzing the eigenvalue spectrum. Delay induced Hopf bifurcation is investigated by using time delay as bifurcation parameter. Some conditions for determining the property of Hopf bifurcation are obtained by utilizing the normal form method and center manifold reduction for partial functional differential equation. 相似文献
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Jia-Fang Zhang 《Applied Mathematical Modelling》2012,36(3):1219-1231
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. 相似文献
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Stability and bifurcation in a delayed predator-prey system with Beddington-DeAngelis functional response 总被引:1,自引:0,他引:1
Zhihua Liu 《Journal of Mathematical Analysis and Applications》2004,296(2):521-537
We consider a delayed predator-prey system with Beddington-DeAngelis functional response. The stability of the interior equilibrium will be studied by analyzing the associated characteristic transcendental equation. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay τ crosses some critical values. The direction and stability of the Hopf bifurcation are investigated by following the procedure of deriving normal form given by Faria and Magalhães. An example is given and numerical simulations are performed to illustrate the obtained results. 相似文献