Spatiotemporal Complexity of a Self- and Cross-Diffusions Predator-Prey System with Ivlev Functional Response

This paper examines the emergence of complex dynamics in a predator-prey system characterized by the Ivlev functional response and influenced by both self- and cross-diffusion. We analytically derive the conditions for the occurrence of Hopf, Turing, and wave bifurcations within a spatially extended domain. Additionally, we provide a theoretical investigation into the evolutionary processes that shape the spatial distribution and interactions of populations undergoing local diffusion. Through numerical simulations, we uncover a diverse range of spatiotemporal patterns, including spots, spirals, and other regular and irregular structures. Our results reveal that the inclusion of spatial effects leads to richer and more intricate dynamics, such as irregular behavior and spiral wave formation. These insights contribute to a deeper understanding of the ecological dynamics.