Qualitative analysis on a diffusive predator-prey model with toxins

This paper is concerned with the diffusive predator-prey model with toxins subject to Dirichlet boundary conditions. The uniform persistence of positive solution is given under certain conditions. In addition, by the Liapunov-Schmidt method, the existence and stability of the bifurcation solution fr...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 486; no. 1; p. 123868
Main Authors Yan, Xiao, Li, Yanling, Guo, Gaihui
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.2020
Subjects
Bifurcation
Multiplicity
Predator-prey model
Uniform persistence
Uniqueness
Bifurcation
Uniform persistence
Predator-prey model
Multiplicity
Uniqueness
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Summary:This paper is concerned with the diffusive predator-prey model with toxins subject to Dirichlet boundary conditions. The uniform persistence of positive solution is given under certain conditions. In addition, by the Liapunov-Schmidt method, the existence and stability of the bifurcation solution from a double eigenvalues are investigated. Moreover, by the fixed point index theory and perturbation theory of eigenvalues, the uniqueness, stability and multiplicity of coexistence states are analyzed when some key parameter changes. Finally, some numerical simulations are presented to verify the theoretical conclusions and further to reflect the importance of parameters to the number of coexistence states.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2020.123868