Lotka-Volterra systems with stochastic resetting

TL;DR

This paper models predator-prey dynamics with predators exhibiting Levy flight dispersal and stochastic resetting to prey patches, revealing optimal conditions for predator abundance and extended species coexistence.

Contribution

It introduces a novel stochastic resetting mechanism into Lotka-Volterra models with Levy dispersal, analyzing its impact on predator-prey dynamics and coexistence.

Findings

Optimal resetting rate maximizes predator population.

Existence of an optimal Levy exponent for predator abundance.

Resetting and Levy dispersal extend species coexistence regions.

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 (L\'evy) dispersal kernel. Site fidelity, an important feature of animal behaviour, is incorporated in the model through a stochastic resetting dynamics of the predators to the prey patch. We solve in the long time limit the rate equations of Lotka-Volterra type that describe the evolution of the two species densities. Fixing the demographic parameters and the L\'evy exponent, the total population of predators can be maximized for a certain value of the resetting rate. This optimal value achieves a compromise between over-exploitation and under-utilization of the habitat. Similarly, at fixed resetting rate, there exists a L\'evy exponent which 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 resources scarcity.