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A Lotka-Volterra symbiotic model with cross-diffusion |
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| Authors: | M Delgado A Suárez |
| Institution: | a Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Fac. de Matemáticas, Univ. de Sevilla, C/. Tarfia s/n, 41012 Sevilla, Spain b Universidade Estadual de Campinas, IMECC, Departamento de Matemática, Caixa Postal 6065, CEP 13083-970, Campinas, SP, Brazil |
| Abstract: | The main goal of this paper is to study the existence and non-existence of coexistence states for a Lotka-Volterra symbiotic model with cross-diffusion. We use mainly bifurcation methods and a priori bounds to give sufficient conditions in terms of the data of the problem for the existence of positive solutions. We also analyze the profiles of the positive solutions when the cross-diffusion parameter goes to infinity. |
| Keywords: | Cross-diffusion Symbiotic model Bifurcation method A priori bounds |
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