Predator prey model with prey harvesting and intraspecific predator competition: spatial–temporal pattern formation via cross-diffusion and periodic dynamics under non-autonomous factors

In this talk, we develop a predator prey model that incorporates logistic prey growth, linear predation, proportional harvesting, and predator intraspecific competition. Starting from an autonomous ordinary differential equation (ODE) model, we extend it to reaction–diffusion (RD) systems with self and cross diffusions to capture random and directed movement of populations respectively. To account for seasonal and anthropogenic influences, we formulate a non-autonomous ODE model with periodic parameters. We analyze the autonomous system’s equilibria, investigate stability under self-diffusion, and derive conditions for Turing instability induced by cross-diffusion. For the non-autonomous system, we employ coincidence degree theory to establish the existence of positive periodic solutions. Numerical simulations illustrate the emergence of spatial patterns under cross-diffusion and the impact of temporal variations on population dynamics.