Bifurcation Branch in a Spatial Heterogeneous Predator–Prey Model with a Nonlinear Growth Rate for the Predator
A strongly coupled predator–prey model in a spatially heterogeneous environment with a Holling type-II functional response and a nonlinear growth rate for the predator is considered. Using bifurcation theory and the Lyapunov–Schmidt reduction, we derived a bounded smooth curve formed by the positive...
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-11-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/23/3748 |
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| Summary: | A strongly coupled predator–prey model in a spatially heterogeneous environment with a Holling type-II functional response and a nonlinear growth rate for the predator is considered. Using bifurcation theory and the Lyapunov–Schmidt reduction, we derived a bounded smooth curve formed by the positive solutions and obtained the structure of the bifurcation branches. We also proved that the bounded curve is monotone <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="bold">S</mi></semantics></math></inline-formula>-shaped or fish-hook-shaped (⊂-shaped), as the values of the parameters of the model vary; in the latter case, the model has multiple positive steady-state solutions caused by the spatial heterogeneity of the environment. |
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| ISSN: | 2227-7390 |