Stability switches in a ring-structured predator–prey metapopulation model with dispersal delay

Abstract

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.