Existence and asymptotic behavior of positive solutions for a one-prey and two-competing-predators system with diffusion. (February 2016)

• Record Type: Journal Article
• Authors: Li, Haixia; Li, Yanling; Yang, Wenbin
• Is Part Of: Nonlinear analysis. Volume 27(2016)
• Page Start: 261
• Page End: 282
• Publication Date: 2016-02
• Subjects: Coexistence -- Global attractor -- Fixed point index -- Bifurcation -- Numerical simulation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.07.010
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: A diffusive one-prey and two-competing-predators system under homogeneous Dirichlet boundary conditions is studied. First, we obtain sufficient conditions for the extinction and existence of global attractor of the time-dependent system by means of the comparison principle. Second, we discuss the existence and nonexistence of coexistence states, and give sufficient conditions for the existence of coexistence states by using the fixed point index theory. In addition, we investigate the bifurcation from a double eigenvalue by virtue of space decomposition and implicit function theorem. Finally, some numerical simulations are made to verify and complement the theoretical analysis.