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In this paper, we investigate the emergence of a predator-prey model withBeddington-DeAngelis-type functional response and reaction-diffusion. We derivethe conditions for Hopf and Turing bifurcation on the spatial domain. Based onthe stability and bifurcation analysis, we give the spatial pattern formationvia numerical simulation, i.e., the evolution process of the model near thecoexistence equilibrium point. We find that for the model we consider, pureTuring instability gives birth to the spotted pattern, pure Hopf instabilitygives birth to the spiral wave pattern, and both Hopf and Turing instabilitygive birth to stripe-like pattern. Our results show that reaction-diffusionmodel is an appropriate tool for investigating fundamental mechanism of complexspatiotemporal dynamics. It will be useful for studying the dynamic complexityof ecosystems.

Spatiotemporal pattern formation of Beddington-DeAngelis-type predator-prey model