Title

Chaotic dynamics in a simple predator-prey model with discrete delay

Document Type

Article

Publication Date

1-1-2021

Publication Title

Discrete and Continuous Dynamical Systems - Series B

Volume

26

Issue

1

First Page

191

Last Page

216

DOI

10.3934/dcdsb.2020263

Keywords

Bi-stability, Hopf and saddle-node bifurcation of limit cycles, Mackey-Glass attractor, Period doubling route to chaos, Predator-prey model, Stage-structured model with maturation delay, Uniform persistence

Abstract

A discrete delay is included to model the time between the capture of the prey and its conversion to viable biomass in the simplest classical Gause type predator-prey model that has equilibrium dynamics without delay. As the delay increases from zero, the coexistence equilibrium undergoes a supercritical Hopf bifurcation, two saddle-node bifurcations of limit cycles, and a cascade of period doublings, eventually leading to chaos. The resulting periodic orbits and the strange attractor resemble their counterparts for the Mackey-Glass equation. Due to the global stability of the system without delay, this compli- cated dynamics can be solely attributed to the introduction of the delay. Since many models include predator-prey like interactions as submodels, this study emphasizes the importance of understanding the implications of overlooking delay in such models on the reliability of the model-based predictions, espe- cially since temperature is known to have an effect on the length of certain delays.

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