Dynamics of prey–predator n-species models with density dependent diffusion. (September 2016)

• Record Type: Journal Article
• Authors: Chen, Yujuan
• Is Part Of: Computers & mathematics with applications. Volume 72:issue 6(2016)
• Page Start: 1727
• Page End: 1742
• Publication Date: 2016-09
• Subjects: Predator–prey models -- Degenerate diffusion -- Ratio-dependent reaction -- Dynamical behavior -- Global attractor -- Stability; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.07.034
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: This paper is concerned with the n -species predator–prey models in a bounded domain in two cases, one of which involves n − 1 cooperative preys and the other involves n − 1 competitive preys. In these models, the diffusion coefficients may be density dependent, and the reaction functions include ratio-dependent terms. Some simple conditions are obtained to ensure the dynamical behaviors of the time-dependent solutions in relation to some positive solutions or quasi-solutions of the steady-state problems, which include the existence of these solutions. This dynamical behaviors lead to the coexistence and global attractors of the predator–prey systems. Some numerical simulations are given in the end.