Abstract
In this paper, we study a diffusive predator–prey system with the nonmonotonic response function. The conditions on Hopf bifurcation and Turing instability of spatial systems are obtained. Near the Turing bifurcation point we apply the weakly nonlinear analysis to derive the amplitude equations of stationary pattern, to investigate the selection of spatiotemporal pattern. It shows that different types of patterns will occur in the model under various conditions. Numerical simulations agree well with our theoretical analysis when control parameters are in the Turing space. This study may provide some deep insights into the formation and selection of patterns for diffusive predator–prey systems.
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