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arXiv · 2007.16140

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

Guihong Fan·Gail S. K. Wolkowicz
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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, eventu1ally 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, these complicated 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, especially since the temperature is known to have an effect on the length of certain delays.

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Guihong Fan, Gail S. K. Wolkowicz. 2020-07-31. Chaotic dynamics in a simple predator-prey model with discrete delay. https://arxiv.org/abs/2007.16140

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