Abstract
We develop a predator prey model with 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 systems to capture spacial movement of populations. Periodic and non-autonomous equations incorporate seasonal and anthropogenic effects. We formulate a non-autonomous differential model with periodic parameters. We analyze the equilibrium stability, and derive conditions for Turing instability. We use coincidence degree theory to show the existence of positive periodic solutions. Numerical simulations illustrate spatial pattern formation and the influence of parameters on population dynamics.