Stationary patterns of a prey–predator system with a protection zone and cross-diffusion of fractional type. (1st April 2019)

• Record Type: Journal Article
• Authors: Li, Shanbing; Dong, Yaying
• Is Part Of: Computers & mathematics with applications. Volume 77:issue 7(2019)
• Page Start: 1873
• Page End: 1887
• Publication Date: 2019-04-01
• Subjects: Fractional type cross-diffusion -- Protection zone -- Coexistence solutions -- Bifurcation -- Asymptotic behavior; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.11.026
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: 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.