Dynamics of two competing species in the presence of Lévy noise sources

Abstract

We consider a Lotka-Volterra system of two competing species subject to multiplicative alpha-stable Lévy noise. The interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence both of a periodic driving term and an additive alpha-stable Lévy noise. We study the species dynamics, which is characterized by two different regimes, exclusion of one species and coexistence of both. We find quasi-periodic oscillations and stochastic resonance phenomenon in the dynamics of the competing species, analysing the role of the Lévy noise sources.