Noise Induced Phenomena in Lotka-Volterra Systems

TL;DR

This paper investigates how external noise and periodic forcing influence two different ecosystems modeled by generalized Lotka-Volterra equations, revealing noise-induced oscillations, resonance, delayed extinction, and spatial pattern formation.

Contribution

It introduces a generalized LV model to analyze noise effects on ecosystems, highlighting phenomena like stochastic resonance and initial condition dependence in spatial patterns.

Findings

Noise induces quasi-deterministic oscillations

Stochastic resonance observed in ecosystems

Spatial patterns depend on initial conditions

Abstract

We study the time evolution of two ecosystems in the presence of external noise and climatic periodical forcing by a generalized Lotka-Volterra (LV) model. In the first ecosystem, composed by two competing species, we find noise induced phenomena such as: (i) quasi deterministic oscillations, (ii) stochastic resonance, (iii) noise delayed extinction and (iv) spatial patterns. In the second ecosystem, composed by three interacting species (one predator and two preys), using a discrete model of the LV equations we find that the time evolution of the spatial patterns is strongly dependent on the initial conditions of the three species.