Global Behavior of Solutions in a Predator-Prey Cross-Diffusion Model with Cannibalism. (22nd May 2020)

• Record Type: Journal Article
• Authors: Chen, Meijun; Fu, Shengmao; Yang, Xiaoli
• Other Names: Gambuzza Lucia Valentina Academic Editor.
• Is Part Of: Complexity. Volume 2020(2020)
• Publication Date: 2020-05-22
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2020/1265798
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : The global asymptotic behavior of solutions in a cross-diffusive predator-prey model with cannibalism is studied in this paper. Firstly, the local stability of nonnegative equilibria for the weakly coupled reaction-diffusion model and strongly coupled cross-diffusion model is discussed. It is shown that the equilibria have the same stability properties for the corresponding ODE model and semilinear reaction-diffusion model, but under suitable conditions on reaction coefficients, cross-diffusion-driven Turing instability occurs. Secondly, the uniform boundedness and the global existence of solutions for the model with SKT-type cross-diffusion are investigated when the space dimension is one. Finally, the global stability of the positive equilibrium is established by constructing a Lyapunov function. The result indicates that, under certain conditions on reaction coefficients, the model has no nonconstant positive steady state if the diffusion matrix is positive definite and the self-diffusion coefficients are large enough.