A History-Dependent Stochastic Predator-Prey Model : Chaos and its Elimination

TL;DR

This paper introduces a non-Markovian stochastic predator-prey model demonstrating how chaos arises and can be eliminated by adjusting interaction rates, with analysis via mean-field approximation and simulations.

Contribution

It presents a novel non-Markovian predator-prey model and shows how chaos can be controlled through interaction rate adjustments based on simulation data.

Findings

Bifurcations lead to chaos in the model

Adjusting interaction rates can eliminate chaos

Correlations between species influence dynamics

Abstract

A non-Markovian stochastic predator-prey model is introduced in which the prey are immobile plants and predators are diffusing herbivors. The model is studied by both mean-field approximation (MFA)and computer simulations. The MFA results a series of bifurcations in the phase space of mean predator and prey densities, leading to a chaotic phase. Because of emerging correlations between the two species distributions, the interaction rate alters and if it is set the value which is obtained from the simulation, then the chaotic phase disappears.