Global Behavior of Solutions in a Predator-Prey Cross-Diffusion Model with Cannibalism
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/1265798 |
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| Summary: | 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. |
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| ISSN: | 1076-2787 1099-0526 |