## Spatiotemporal dynamics of a Leslie-Gower predator-prey model incorporating a prey refuge.(English)Zbl 1225.49038

Summary: We investigate the spatiotemporal dynamics of a two-dimensional predator-prey model, which is based on a modified version of the Leslie-Gower scheme incorporating a prey refuge. We establish a Lyapunov function to prove the global stability of the equilibria with diffusion and determine the Turing space in the spatial domain. Furthermore, we perform a series of numerical simulations and find that the model dynamics exhibits complex Turing pattern replication: stripes, cold/hot spots-stripes coexistence and cold/hot spots patterns. The results indicate that the effect of the prey refuge for pattern formation is tremendous. This may enrich the dynamics of the effect of refuge on predator-prey systems.

### MSC:

 49N75 Pursuit and evasion games 93C20 Control/observation systems governed by partial differential equations 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory
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### References:

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