A nonlinear $L^2$-stability analysis for two-species population dynamics with dispersal
The nonlinear $L^2$-stability (instability) of the equilibrium statesof two-species population dynamics with dispersal is studied. The obtainedresults are based on (i) the rigorous reduction of the $L^2$-nonlinear stability tothe stability of the zero solution of a linear binary system of ODEs and (...
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| Language: | English |
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AIMS Press
2005-10-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.189 |
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| _version_ | 1832590287348695040 |
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| author | Salvatore Rionero |
| author_facet | Salvatore Rionero |
| author_sort | Salvatore Rionero |
| collection | DOAJ |
| description | The nonlinear $L^2$-stability (instability) of the equilibrium statesof two-species population dynamics with dispersal is studied. The obtainedresults are based on (i) the rigorous reduction of the $L^2$-nonlinear stability tothe stability of the zero solution of a linear binary system of ODEs and (ii) theintroduction of a particular Liapunov functional V such that the sign of$\frac{dV}{dt}$ along the solutions is linked directly to the eigenvalues of the linear problem. |
| format | Article |
| id | doaj-art-cdb106c500534ff6a7a7730f67a91945 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2005-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-cdb106c500534ff6a7a7730f67a919452025-01-24T01:51:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182005-10-013118920410.3934/mbe.2006.3.189A nonlinear $L^2$-stability analysis for two-species population dynamics with dispersalSalvatore Rionero0University of Naples Federico II, Department of Mathematics and Applications ''R. Caccioppoli", Complesso Universitario Monte S. Angelo. Via Cinzia, 80126 NapoliThe nonlinear $L^2$-stability (instability) of the equilibrium statesof two-species population dynamics with dispersal is studied. The obtainedresults are based on (i) the rigorous reduction of the $L^2$-nonlinear stability tothe stability of the zero solution of a linear binary system of ODEs and (ii) theintroduction of a particular Liapunov functional V such that the sign of$\frac{dV}{dt}$ along the solutions is linked directly to the eigenvalues of the linear problem.https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.189liapunov direct methodnonlinear stabilityreaction diffusion equations.two-species population dynamics |
| spellingShingle | Salvatore Rionero A nonlinear $L^2$-stability analysis for two-species population dynamics with dispersal Mathematical Biosciences and Engineering liapunov direct method nonlinear stability reaction diffusion equations. two-species population dynamics |
| title | A nonlinear $L^2$-stability analysis for two-species population dynamics with dispersal |
| title_full | A nonlinear $L^2$-stability analysis for two-species population dynamics with dispersal |
| title_fullStr | A nonlinear $L^2$-stability analysis for two-species population dynamics with dispersal |
| title_full_unstemmed | A nonlinear $L^2$-stability analysis for two-species population dynamics with dispersal |
| title_short | A nonlinear $L^2$-stability analysis for two-species population dynamics with dispersal |
| title_sort | nonlinear l 2 stability analysis for two species population dynamics with dispersal |
| topic | liapunov direct method nonlinear stability reaction diffusion equations. two-species population dynamics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.189 |
| work_keys_str_mv | AT salvatorerionero anonlinearl2stabilityanalysisfortwospeciespopulationdynamicswithdispersal AT salvatorerionero nonlinearl2stabilityanalysisfortwospeciespopulationdynamicswithdispersal |