The 3‐D bifurcation and limit cycles in a food‐chain model |
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| Authors: | Lemin Zhu Xuncheng Huang |
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| Institution: | Yangzhou Polytechnic University, Yangzhou, Jiangsu 225009, People's Republic of China |
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| Abstract: | In this paper, by using a corollary to the center manifold theorem, we show that the 3‐D food‐chain model studied by many authors undergoes a 3‐D Hopf bifurcation, and then we obtain the existence of limit cycles for the 3‐D differential system. The methods used here can be extended to many other 3‐D differential equation models. Copyright © 2008 John Wiley & Sons, Ltd. |
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| Keywords: | Hopf bifurcation food chain Lyapunov function center manifold theorem limit cycles |
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