Lotka–Volterra systems with stochastic resetting

Abstract

We study the dynamics of predator–prey systems where prey are confined to a single region of space and where predators move randomly according to a power-law (Lévy) dispersal kernel. Site fidelity, an important feature of animal behavior, is incorporated in the model through stochastic resetting dynamics of the predators to the prey patch. We solve in the long time limit the Lotka–Volterra rate equations that describe the evolution of the two species’ densities. Fixing the demographic parameters and the Lévy exponent, the total population of predators can be maximized for a certain value of the resetting rate. This optimal value achieves a compromise between the overexploitation and underutilization of the habitat. Similarly, at a fixed resetting rate, there exists a Lévy exponent that is optimal regarding predator abundance. These findings are supported by 2D stochastic simulations and show that the combined effects of diffusion and resetting can broadly extend the region of species coexistence in ecosystems facing resource scarcity.