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Spatiotemporal complexity of a predator-prey system with constant harvest rate. (English) Zbl 1198.35127

Summary: We investigate the emergence of a predator-prey system with Michaelis-Menten-type predator-prey systems with reaction-diffusion and constant harvest rate. We derive the conditions for Hopf and Turing bifurcation on the spatial domain. The results of spatial pattern analysis, via numerical simulations, typical spatial pattern formation is isolated groups, i.e., stripe-like, patch-like and so on. Our results show that modeling by reaction-diffusion equations is an appropriate tool for investigating fundamental mechanisms of complex spatiotemporal dynamics. It will be useful for studying the dynamic complexity of ecosystems.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:

35K57 Reaction-diffusion equations
92D25 Population dynamics (general)
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