BIFURCATION ANALYSIS OF A LOGISTIC PREDATOR-PREY SYSTEM WITH DELAY

被引：0

作者：

Celik, Canan ^{[1
]}

Cekic, Gokcen ^{[2
]}

机构：

[1] Bahcesehir Univ, Fac Engn & Nat Sci, TR-34353 Istanbul, Turkey

[2] Istanbul Univ, Dept Math, TR-34134 Istanbul, Turkey

来源：

ANZIAM JOURNAL | 2016年 / 57卷 / 04期

关键词：

predator-prey system; delayed logistic differential equation; Hopf bifurcation; stability; GLOBAL PERIODIC-SOLUTIONS; HOPF-BIFURCATION; STABILITY; MODEL;

D O I：

10.21914/anziamj.v57i0.9441

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a coupled, logistic predator-prey system with delay. Mainly, by choosing the delay time tau as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay time tau passes some critical values. Based on the normal-form theory and the centre manifold theorem, we also derive formulae to obtain the direction, stability and the period of the bifurcating periodic solution at critical values of tau. Finally, numerical simulations are investigated to support our theoretical results.

引用

页码：445 / 460

页数：16

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