Abstract
In this paper, we consider a predator–prey metapopulation model with a ring-structured configuration of an arbitrary and finite number of patches. The prey are assumed to disperse between the connected patches with a constant dispersal delay. We show that the dispersal delay can induce stability switches exhibiting both stabilizing and destabilizing roles in the stability of the symmetric coexistence equilibrium. Numerical simulations are presented to further illustrate the effects of the dispersal delay, the dispersal rate, the fraction of dispersal due to predation avoidance and the network topology on the number of stability switches.
Highlights
The predator–prey relationship is one of the fundamental relationships in ecological systems and has been extensively studied in the literature [1]
Many mathematical models have been proposed to study the impacts of dispersal over patches on metacommunity dynamics
6 Summary In this paper, we have considered a metapopulation predator–prey model with delayed dispersal within a ring-structured configuration of network topology
Summary
The predator–prey relationship is one of the fundamental relationships in ecological systems and has been extensively studied in the literature [1]. It is well known that the coexistence equilibrium En∗ of system (2.2) is stable if and only if all characteristic roots of (3.5) have negative real parts [25]. This shows that purely imaginary roots of the characteristic equations (3.5) under condition (1) are obtained at the following sequences of positive values of τ : τl(,k1)
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