Turing instability for a competitor-competitor-mutualist model with nonlinear cross-diffusion effects. (October 2016)

• Record Type: Journal Article
• Authors: Wen, Zijuan; Fu, Shengmao
• Is Part Of: Chaos, solitons and fractals. Volume 91(2016)
• Page Start: 379
• Page End: 385
• Publication Date: 2016-10
• Subjects: Competitor-competitor-mutualist -- Cross-diffusion -- Persistence -- Turing instability -- Global asymptotic stability; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2016.06.019
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: This paper deals with a strongly coupled reaction-diffusion system modeling a competitor-competitor-mutualist three-species model with diffusion, self-diffusion and nonlinear cross-diffusion and subject to Neumann boundary conditions. First, we establish the persistence of a corresponding reaction-diffusion system without self- and cross-diffusion. Second, the global asymptotic stability of the unique positive equilibrium for weakly coupled PDE system is established by using a comparison method. Moreover, under certain conditions about the intra- and inter-species effects, we prove that the uniform positive steady state is linearly unstable for the cross-diffusion system when one of the cross-diffusions is large enough. The results indicate that Turing instability can be driven solely from strong diffusion effect of the first species (or the second species or the third species) due to the pressure of the second species (or the first species).