Stability, delay, and chaotic behavior in a Lotka-Volterra predator-prey system

被引：0

作者：

Nakaoka, S ^{[1
]}

Saito, Y ^{[1
]}

Takeuchi, Y ^{[1
]}

机构：

[1] Shizuoka Univ, Fac Engn, Dept Syst Engn, Hamamatsu, Shizuoka 4328561, Japan

来源：

MATHEMATICAL BIOSCIENCES AND ENGINEERING | 2006年 / 3卷 / 01期

关键词：

predator-prey; subcritical Hopf bifurcation; chaotic behavior; mathematical model; nonlinear dynamics;

D O I：

暂无

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We consider the following Lotka-Volterra predator-prey system with two delays: {chi '(t) = chi(t) [r(1) - a chi (t - tau(1)) - by(t)] {y '(t) = y(t) [-r(2) + c chi(t) - dy(t - tau(2))]. (E) We show that a positive equilibrium of system (E) is globally asymptotically stable for small delays. Critical values of time delay through which system (E) undergoes a Hopf bifurcation are analytically determined. Some numerical simulations suggest an existence of subcritical Hopf bifurcation near the critical values of time delay. Further system (E) exhibits some chaotic behavior when tau(2) becomes large.

引用

页码：173 / 187

页数：15

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