Bifurcation analysis and control of chaos for a hybrid ratio-dependent three species food chain |
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| Authors: | Huitao Zhao Yiping Lin Yunxian Dai |
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| Affiliation: | a Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, China
b Department of Mathematics and Information Science, Zhoukou Normal University, Zhoukou, Henan 466001, China |
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| Abstract: | In this paper, a hybrid ratio-dependent three species food chain model with time delay is studied by using the theory of functional differential equation and Hopf bifurcation, the condition on which positive equilibrium exists and the quality of Hopf bifurcation are given. Chaotic solutions are observed and are controlled by delay parameter. Finally, we indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable state or a stable periodic orbit. |
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| Keywords: | Three species food chain Hybrid ratio-dependent response Bifurcation analysis Chaos control |
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