Transition from stationary patterns to no-stationary patterns in a predator–prey system

Pattern structures are indicators of populations distribution and may provide some signals for population protection. In this paper, we present a predator–prey system with spatial diffusion and ratio-dependent functional response. Based on both mathematical analysis and numerical simulations, we find that predation rate of predator plays an important role in pattern formation of populations. As it varies, transition from stationary patterns to no-stationary patterns emerges. Th e obtained results show that predation behavior of predator on prey is a key determinant in the persistence of populations.