$n$-dimensional ratio-dependent predator-prey systems with memory

TL;DR

This paper studies high-dimensional predator-prey models with ratio dependence and delay, analyzing conditions where delay does not cause instability and providing examples where it does.

Contribution

It offers new insights into the stability of complex predator-prey systems with delay, identifying conditions preventing delay-induced instability.

Findings

Delay does not always cause instability in high-dimensional systems

Conditions for stability in ratio-dependent predator-prey models with delay

An example demonstrating delay-induced instability

Abstract

This paper deals with ratio-dependent predator-prey systems with delay. We will investigate under what conditions delay cannot cause instability in higher dimension. We give an example when delay causes instability.