Spatiotemporal patterns induced by delay and cross-fractional diffusion in a predator-prey model describing intraguild predation |
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Authors: | Zhan-Ping Ma Hai-Feng Huo Hong Xiang |
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Affiliation: | 1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454003 Henan, People's Republic of China;2. Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, 730050 Gansu, People's Republic of China |
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Abstract: | In this article, we study a reaction-diffusion predator-prey model that describes intraguild predation. We mainly consider the effects of time delay and cross-fractional diffusion on dynamical behavior. By using delay as the bifurcation parameter, we perform a detailed Hopf bifurcation analysis and derive the algorithm for determining the direction and stability of the bifurcating periodic solutions. We also demonstrate that proper cross-fractional diffusion can induce Turing pattern, and the smaller the order of fractional diffusion is, the more easily Turing pattern is able to occur. |
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Keywords: | cross-fractional diffusion delay Hopf bifurcation predator-prey Turing pattern |
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