Complexity in a prey-predator model with prey refuge and diffusion

Abstract

Prey-predator interaction is one of the most commonly observed relationships in ecosystem. In the study of prey-predator models, it is frequently assumed that the changes in population densities are only time-dependent and the dynamics is generally represented by coupled nonlinear ordinary differential equations. In natural system, however, either prey or predator or both move from one place to another for various reasons. In such a case, their dynamic interaction depends both on time and space and requires coupled nonlinear partial differential equations for its dynamic representation. It is also well documented that prey refuges affect the interaction between prey and predator significantly. In this paper, we studied the dynamics of a diffusive prey-predator interaction with prey refuge and type III response function. We have considered both one and two dimensional diffusivity in the model system and presented different stability results under the assumptions that one or both species may be mobile or sedentary. Our results showed that the system may exhibit different spatiotemporal (non-Turing) patterns, like spiral waves, patchy structures, spot pattern, or even spatiotemporal chaos depending on the refuge availability and diffusion rate of species. Another interesting finding was that the dynamic complexity in a prey-predator model increases in case of mobile predator and sedentary prey compare to mobile prey and sedentary predator while refuge availability is varied.