Stability and Hopf Bifurcation in a Three-Species Food Chain System With Harvesting and Two Delays-Reference-Cited by-同舟云学术

Stability and Hopf Bifurcation in a Three-Species Food Chain System With Harvesting and Two Delays

Published:2014-01-09 Issue:2 Volume:9 Page:
ISSN:1555-1415
Container-title:Journal of Computational and Nonlinear Dynamics
language:en
Short-container-title:

Author:

Zhang Zizhen¹²,Yang Huizhong³

Affiliation:

1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China

2. School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China e-mail:

3. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China e-mail:

Abstract

In this paper, we analyze the dynamics of a delayed food chain system with harvesting. Sufficient conditions for the local stability of the positive equilibrium and for the existence of Hopf bifurcation are obtained by analyzing the associated characteristic equation. Formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis.

Publisher

ASME International

Subject

Applied Mathematics,Mechanical Engineering,Control and Systems Engineering,Applied Mathematics,Mechanical Engineering,Control and Systems Engineering

Link

http://asmedigitalcollection.asme.org/computationalnonlinear/article-pdf/doi/10.1115/1.4025670/6103916/cnd_009_02_024501.pdf

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