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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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/1265798 |
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| _version_ | 1832547172266016768 |
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| author | Meijun Chen Shengmao Fu Xiaoli Yang |
| author_facet | Meijun Chen Shengmao Fu Xiaoli Yang |
| author_sort | Meijun Chen |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b359f295b42042d3bb8a67c10c74ca4e |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-b359f295b42042d3bb8a67c10c74ca4e2025-02-03T06:45:59ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/12657981265798Global Behavior of Solutions in a Predator-Prey Cross-Diffusion Model with CannibalismMeijun Chen0Shengmao Fu1Xiaoli Yang2College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaThe 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.http://dx.doi.org/10.1155/2020/1265798 |
| spellingShingle | Meijun Chen Shengmao Fu Xiaoli Yang Global Behavior of Solutions in a Predator-Prey Cross-Diffusion Model with Cannibalism Complexity |
| title | Global Behavior of Solutions in a Predator-Prey Cross-Diffusion Model with Cannibalism |
| title_full | Global Behavior of Solutions in a Predator-Prey Cross-Diffusion Model with Cannibalism |
| title_fullStr | Global Behavior of Solutions in a Predator-Prey Cross-Diffusion Model with Cannibalism |
| title_full_unstemmed | Global Behavior of Solutions in a Predator-Prey Cross-Diffusion Model with Cannibalism |
| title_short | Global Behavior of Solutions in a Predator-Prey Cross-Diffusion Model with Cannibalism |
| title_sort | global behavior of solutions in a predator prey cross diffusion model with cannibalism |
| url | http://dx.doi.org/10.1155/2020/1265798 |
| work_keys_str_mv | AT meijunchen globalbehaviorofsolutionsinapredatorpreycrossdiffusionmodelwithcannibalism AT shengmaofu globalbehaviorofsolutionsinapredatorpreycrossdiffusionmodelwithcannibalism AT xiaoliyang globalbehaviorofsolutionsinapredatorpreycrossdiffusionmodelwithcannibalism |