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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 12
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Articles

Bifurcation behaviours in a delayed three-species food-chain model with Holling type-II functional response

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Pages 2468-2486 | Received 02 Jun 2012, Accepted 07 Oct 2012, Published online: 14 Dec 2012
 

Abstract

This article is concerned with the local stability of a positive equilibrium and the Hopf bifurcation of a delayed three-species food-chain system with the Holling type-II functional response. Some new sufficient conditions ensuring the local stability of a positive equilibrium and the existence of Hopf bifurcation for the system are established. Some explicit formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions using the normal form theory and the centre manifold theory. Numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are included.

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Acknowledgement

This work is supported by National Natural Science Foundation of China(No.11261010, No.10961008), Soft Science and Technology Program of Guizhou Province(No.2011LKC2030), Natural Science and Technology Foundation of Guizhou Province(J[2012]2100), Governor Foundation of Guizhou Province([2012]53) and Doctoral Foundation of Guizhou University of Finance and Economics (2010).

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