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 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 graham c+ cream patterns.One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay goodridge 24215 brake line 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.