Bifurcation analysis for a three-species predator-prey system with two delays |
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Authors: | Maoxin Liao Xianhua TangChangjin Xu |
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Institution: | a School of Mathematics and Physics, University of South China, Hengyang, Hunan 421001, PR China b School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410083, PR China |
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Abstract: | In this paper, a three-species predator-prey system with two delays is investigated. By choosing the sum τ of two delays as a bifurcation parameter, we first show that Hopf bifurcation at the positive equilibrium of the system can occur as τ crosses some critical values. Second, we obtain the formulae determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions by using the normal form theory and center manifold theorem. Finally, numerical simulations supporting our theoretical results are also included. |
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Keywords: | Predator-prey system Delay Hopf bifurcation Periodic solution |
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