Bifurcations in Delayed Lotka-Volterra Intraguild Predation Model

TL;DR

This paper analyzes a three-species intraguild predation model with delay, exploring how delay affects the existence, stability, and bifurcations of equilibria, revealing complex dynamics including chaos.

Contribution

It introduces a delayed Lotka-Volterra intraguild predation model and characterizes the bifurcation structure influenced by delay, which is a novel analysis in this context.

Findings

Delay influences stability and bifurcation of equilibria.

Conditions for existence and stability of equilibria are derived.

Numerical bifurcation analysis illustrates complex dynamics including chaos.

Abstract

Omnivory is defined as feeding on more than one trophic level. An example of this is the so-called intraguild predation (IG) which includes a predator and its prey that share a common resource. IG predation models are known to exhibit interesting dynamics including chaos. This work considers a three-species food web model with omnivory, where the interactions between the basal resource, the IG prey, and the IG predator are of Lotka-Volterra type. In the absence of predation, the basal resource follows a delayed logistic equation or popularly known as Hutchinson's equation. Conditions for the existence, stability, and bifurcations of all non-negative equilibrium solutions are given using the delay time as parameter. Results are illustrated using numerical bifurcation analysis.