一類具有收獲率競爭系統的穩定性及Hopf分岔

陳紅兵,何萬生

(天水師范學院數學與統計學院,甘肅 天水 741001)

一類具有收獲率競爭系統的穩定性及Hopf分岔

陳紅兵,何萬生

(天水師范學院數學與統計學院,甘肅 天水 741001)

首先建立了一類具有時滯的捕獲率的競爭系統,該系統具有Holling II功能.接著應用特征方程,發現當τ穿過某些數時出現了Hopf分岔,并用規范型方法和中心流形定理得到Hopf分岔和分岔周期解的穩定性的計算公式.最后舉例論證.

競爭;穩定性;平衡點;Hopf分岔

1 引言

受到文獻[1-5]的啟發,本文建立具有收獲率的時滯Holling II功能反應系統:

2 有界性

3 Hopf分岔的存在性

4 Hopf分岔與分岔周期解的計算公式

5 舉例

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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

圖1 τ=1平衡點漸近穩定

圖2 τ=3 Hopf分岔及周期解穩定

O175.14

A

1008-5513(2012)05-0604-10

2012-04-10.

甘肅省自然科學基金(096RJZE106).

陳紅兵(1983-),碩士,講師,研究方向：應用微分方程.

2010 MSC:34D12