Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion

Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion

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We consider the polly pocket pineapple purse effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge.Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns.One of the most interesting findings is that the model exhibits complex pattern replication: goodridge 24215 brake line the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication.The results indicate that time delay and cross diffusion play important roles in pattern formation.