Stationary patterns of a prey-predator system with a protection zone and cross-diffusion of fractional type

摘要

This paper is concerned with the stationary patterns of a prey-predator model with a protection zone and fractional type cross-diffusion for the prey. It is shown that the fractional type cross-diffusion has negative effects on the survival of the prey when the intrinsic growth rate of the predator is positive. Moreover, our mathematical analysis shows that, compared with the results obtained in K. Oeda (2011) and K. Oeda (2012), the large cross-diffusion coefficient and large growth rate of the predator species have some essentially different effects on the profiles of the solutions. (C) 2018 Elsevier Ltd. All rights reserved.