A Diffusive Predator-Prey Model with Group Defense and Memory Effect in Predator

In this study, we investigate a prey-predator model with group defense and memory effect in predator to reveal the joint impact of memory-based diffusion coefficient, the averaged memory period and shape parameter α on population dynamics. For fixed α, spatially inhomogeneous time-periodic solution is generated when memory-based diffusion coefficient and the averaged memory period exceed some critical values. Meanwhile, stability switches induced by α occur when memory-based diffusion coefficient and the averaged memory period are set to certain values. Moreover, we illustrate that the averaged memory period may induce stability switches when α and memory-based diffusion coefficient lie within a specific range. Furthermore, diverse spatiotemporal pattern formations emerge depending on the values of memory-based diffusion coefficient, α and the averaged memory period. Compared with the diffusive predator-prey model with Holling-I function response and memory effect of predator, the model in this paper can produce more intricate dynamics.