Bifurcation Branch in a Spatial Heterogeneous Predator–Prey Model with a Nonlinear Growth Rate for the Predator

Lei Kong ()
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Lei Kong: College of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China

Mathematics, 2024, vol. 12, issue 23, 1-18

Abstract: 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 S -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.

Keywords: positive solution; heterogeneous environment; fish-hook bifurcation; Lyapunov–Schmidt reduction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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