A multi-scale study of a class of hybrid predator-prey models

TL;DR

This paper investigates a multi-scale hybrid predator-prey model where prey dynamics are fast differential equations and predator dynamics are jump processes, deriving an averaged model and comparing it to the original system.

Contribution

It introduces an averaging principle for coupled differential and jump process predator-prey models with different time scales.

Findings

Averaged model accurately approximates the original system.

Comparison shows the averaged model captures key probabilistic behaviors.

Results demonstrate effectiveness of averaging in hybrid systems.

Abstract

We address the question of an averaging principle for a general class of multi-scale hybrid predator-prey models. We consider prey-predator models where the kinetic of the prey population, described by a differential equation, is faster than the kinetic of the predator population, described by a jump process, the two dynamics being fully coupled. An averaged model is obtained and compared to the original slow-fast system in term of probability and absorption time.