Dynamics of predator-prey systems with prey’s dispersal between patches

Jiale Ban, Yuanshi Wang and Hong Wu ()
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Jiale Ban: Sun Yat-sen University
Yuanshi Wang: Sun Yat-sen University
Hong Wu: Sun Yat-sen University

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 2, 550-569

Abstract: Abstract This paper analyzes dispersal in predator-prey systems, where the prey can move between a source and a sink patch and the predation interaction is described by the Holling II functional response. By applying dynamical systems theory, we present a complete study on persistence of the system, and show local/global stability of equilibria. Then we prove Hopf bifurcation in the system by computing Lyapunov coefficient, and show that dispersal could lead to results reversing those if non-dispersing. By explicit expressions of stable equilibria, we show that dispersal could make the prey approach total abundance larger than if non-dispersing, even larger than its carrying capacity when the predator persists. Asymmetry in dispersal could also lead to the results. Total abundance of the prey is shown to be a distorted function (surface) of dispersal rates, which extends both previous theory and experimental observations. It is proven that there exists an optimal dispersal that drives the predator into extinction and makes the prey reach the maximal abundance. These results are biologically important in preserving endangered species.

Keywords: Predation; Lyapunov coefficient; Hopf bifurcation; Diffusion; Stability; 34C12; 37N25; 34C28; 37G20 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13226-021-00117-5

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