Global Behavior of Solutions in a Predator-Prey Cross-Diffusion Model with Cannibalism

Meijun Chen, Shengmao Fu and Xiaoli Yang

Complexity, 2020, vol. 2020, 1-19

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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:1265798

DOI: 10.1155/2020/1265798

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