Global Bifurcation in a General Leslie Type Predator–Prey System with Prey Taxis
In this paper, the local and global structure of positive solutions for a general predator–prey model in a multi-dimension with ratio-dependent predator influence and prey taxis is investigated. By analyzing the corresponding characteristic equation, we first obtain the local stability conditions of...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/4/238 |
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| Summary: | In this paper, the local and global structure of positive solutions for a general predator–prey model in a multi-dimension with ratio-dependent predator influence and prey taxis is investigated. By analyzing the corresponding characteristic equation, we first obtain the local stability conditions of the positive equilibrium caused by prey taxis. Secondly, taking the prey-taxis coefficient as a bifurcation parameter, we obtain the local structure of the positive solution by resorting to an abstract bifurcation theorem, and then extend the local solution branch to a global one. Finally, the local stability of such bifurcating positive solutions is discussed by the method of the perturbation of simple eigenvalues and spectrum theory. The results indicate that attractive prey taxis can stabilize positive equilibrium and inhibits the emergence of spatial patterns, while repulsive prey taxis can lead to Turing instability and induces the emergence of spatial patterns. |
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| ISSN: | 2075-1680 |