Turing patterns of a strongly coupled predator-prey system with diffusion effects |
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Authors: | Jia-Fang ZhangWan-Tong Li Yu-Xia Wang |
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Institution: | School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China |
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Abstract: | The main purpose of this work is to investigate the effects of cross-diffusion in a strongly coupled predator-prey system. By a linear stability analysis we find the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, it is shown that Turing instability of the reaction-diffusion system can disappear due to the presence of the cross-diffusion, which implies that the cross-diffusion induced stability can be regarded as the cross-stability of the corresponding reaction-diffusion system. Furthermore, we consider the existence and non-existence results concerning non-constant positive steady states (patterns) of the system. We demonstrate that cross-diffusion can create non-constant positive steady-state solutions. These results exhibit interesting and very different roles of the cross-diffusion in the formation and the disappearance of the Turing instability. |
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Keywords: | 35J55 35K57 92D25 |
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