Cross-diffusion-induced instabilities in a cooperative hunting population with Allee effect

The spatiotemporal complexity of a system of interacting species, influenced by hunting cooperation and the additive Allee effect, has garnered significant attention within the ecological framework. This study investigates whether interactions among species can stabilize the dynamics of environmental communities and promote coexistence, employing a cross-diffusion-driven species interaction model. The local and global bifurcation behaviour of the proposed system and the stability of all potential equilibrium points in the absence of diffusion have been comprehensively examined. Numerical simulations have been conducted to validate the analytical findings and assess the applicability of the cross-diffusive model. In a two-dimensional plane, the evolution of diffusion-driven pattern generation, known as black-eye replication, around the coexistence equilibrium point has been presented. Furthermore, it has been demonstrated that species interactions within the context of cross-diffusion can exacerbate the instability dynamics of ecological populations by generating spatial patterns. The results underscore the crucial role of cross-diffusion-driven instability in maintaining ecosystem diversity and structure.