Effects of the self- and cross-diffusion on positive steady states for a generalized predator–prey system. (December 2016)

• Record Type: Journal Article
• Authors: Jia, Yunfeng; Xue, Pan
• Is Part Of: Nonlinear analysis. Volume 32(2016)
• Page Start: 229
• Page End: 241
• Publication Date: 2016-12
• Subjects: Predator–prey system -- Self- and cross-diffusion -- Positive steady states -- Stability -- Leray–Schauder degree; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.04.012
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper deals with a generalized predator–prey system with cross-diffusion and homogeneous Neumann boundary condition, where the cross-diffusion is included in such a way that the prey runs away from the predator. We first give a priori estimate for positive steady states to the system. Then we obtain the non-existence result of non-constant positive steady states. Finally, we investigate the stability of constant equilibrium point and the existence of non-constant positive steady states. It is shown that the system admits a non-constant positive steady state provided that either of the self-diffusions is large or the cross-diffusion is small.