Delay diffusive prey predator model with hunting cooperation in predators

In this paper, we conduct a detailed stability analysis and investigate Hopf bifurcation in a temporal predator-prey model that incorporates cooperative hunting among predators. Building on this, we extend the model to a spatiotemporal domain to explore how spatial diffusion influences the dynamics. Our simulations reveal distinct spatial patterns, such as cold spots indicating low prey density and hot spots indicating high predator concentration. Notably, we observe that increasing the diffusion rates leads to the formation of more sharply concentrated and spatially structured patterns. To further enrich the model, we introduce a time delay representing the gestation or response time in predator-prey interactions. The inclusion of delay significantly alters the dynamics: while the non-delayed model supports stationary spatial patterns, the delayed model gives rise to complex oscillatory structures that evolve, highlighting the critical role of delay in generating temporal fluctuations in pattern formation.

کلیدواژه ها:

Spatio-temporal predator-prey model ، Delayed spatio-temporal model ، Stability and bifurcation analysis