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Bifurcation analysis for a three-species predator–prey system with two delays

✍ Scribed by Maoxin Liao; Xianhua Tang; Changjin Xu

Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
520 KB
Volume
17
Category
Article
ISSN
1007-5704

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✦ Synopsis

In this paper, a three-species predator-prey system with two delays is investigated. By choosing the sum s of two delays as a bifurcation parameter, we first show that Hopf bifurcation at the positive equilibrium of the system can occur as s crosses some critical values.

Second, we obtain the formulae determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions by using the normal form theory and center manifold theorem. Finally, numerical simulations supporting our theoretical results are also included.

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