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 Formula: see text on population dynamics. For fixed Formula: see text, 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 Formula: see text 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 Formula: see text 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, Formula: see text 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.
Liu et al. (Mon,) studied this question.