Abstract:

Current studies on predator-prey systems mainly consider single interaction mechanisms, which cannot fully characterize the complex ecological interactions between populations. Therefore, this paper establishes a cross-diffusion predator-prey system incorporating multiple interaction mechanisms including fear effects, saturation effects, intraspecific competition, and predator interference, based on the Beddington-DeAngelis functional response function and modified Leslie-Gower terms. For the non-diffusion system, we analyze the stability of positive equilibrium points and the Hopf bifurcation conditions induced by prey intraspecific competition. For the diffusion system, we derive the conditions for Turing instability and focus on investigating how various interaction mechanisms affect the formation and evolution of Turing patterns. The results demonstrate that changing the intensity of interaction mechanisms (such as fear effects) and cross-diffusion coefficients can lead to transitions between different Turing patterns, while different interaction mechanisms can also alter the system stability and the stabilization rate of Turing patterns to varying degrees. The results indicate that interactions between predators and prey, along with cross-diffusion, significantly impact the dynamical behavior of the system.

Key words: interaction, cross-diffusion, Beddington-DeAngelis functional response, modified Leslie-Gower, Turing patterns