一类具有收获率竞争系统的稳定性及Hopf分岔

陈红兵,何万生

(天水师范学院数学与统计学院,甘肃 天水 741001)

一类具有收获率竞争系统的稳定性及Hopf分岔

陈红兵,何万生

(天水师范学院数学与统计学院,甘肃 天水 741001)

首先建立了一类具有时滞的捕获率的竞争系统,该系统具有Holling II功能.接着应用特征方程,发现当τ穿过某些数时出现了Hopf分岔,并用规范型方法和中心流形定理得到Hopf分岔和分岔周期解的稳定性的计算公式.最后举例论证.

竞争;稳定性;平衡点;Hopf分岔

1 引言

受到文献[1-5]的启发,本文建立具有收获率的时滞Holling II功能反应系统:

2 有界性

3 Hopf分岔的存在性

4 Hopf分岔与分岔周期解的计算公式

5 举例

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The Hopf bifurcation and stability of competitive system with rate harvesting

Chen Hongbing,He Wansheng
(School of Mathematics and Statistics Tianshui Normal University,Tianshui741001,China)

First,established a competitive mold with Holling II functional response.Further,by analyzing the associated characteristic equation,it is founded that Hopf bifurcation occurs when τ crosses some critical value. The direction of Hopf bifurcation as well as stability of periodic solution are studied.The method which we used is the normal form theory and center manifold method.An example showed the feasibility of results.

compete,stability,equilibrium point,Hopf bifurcation

图1 τ=1平衡点渐近稳定

图2 τ=3 Hopf分岔及周期解稳定

O175.14

A

1008-5513(2012)05-0604-10

2012-04-10.

甘肃省自然科学基金(096RJZE106).

陈红兵(1983-),硕士,讲师,研究方向：应用微分方程.

2010 MSC:34D12