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| Bogdanov-Takens Bifurcation in a Host-parasitoidModel |
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| KeyWord:Host-parasitoid model Holling II functional response Bogdanov-
Takens bifurcation |
| Author Name | Affiliation | | Chuang Xiang | School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, China | | Ming Lu | School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, China | | Jicai Huang | School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, China |
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| Abstract: |
| In this paper, we study a host-parasitoid model with Holling II Functional response, where we focus on a special case: the carrying capacity K2 for parasitoids is equal to a critical value
r 1η. It is shown that the model can undergo Bogdanov-Takens bifurcation. The approximate expressions for
saddle-node, Homoclinic and Hopf bifurcation curves are calculated. Numerical simulations, including bifurcation diagrams and corresponding phase portraits, are also given to illustrate the theoretical results. |
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