Spiral attractors as the root of a new type of "bursting activity" in the Rosenzweig-MacArthur model

TL;DR

This paper investigates spiral attractors in the Rosenzweig-MacArthur model, revealing their origin via the Shilnikov scenario and identifying a new type of bursting activity characterized by alternating fast and slow oscillations.

Contribution

It uncovers the mechanism behind spiral attractors through bifurcation analysis and introduces a novel bursting activity pattern in the food chain model.

Findings

Spiral attractors originate from a Shilnikov scenario involving bifurcations.

A new type of bursting activity with alternating fast and slow oscillations is identified.

Bursting can be chaotic or regular depending on parameters.

Abstract

We study the peculiarities of spiral attractors in the Rosenzweig-MacArthur model, that describes dynamics in a food chain "prey-predator-superpredator". It is well-known that spiral attractors having a "teacup" geometry are typical for this model at certain values of parameters for which the system can be considered as slow-fast system. We show that these attractors appear due to the Shilnikov scenario, the first step in which is associated with a supercritical Andronov-Hopf bifurcation and the last step leads to the appearance of a homoclinic attractor containing a homoclinic loop to a saddle-focus equilibrium with two-dimension unstable manifold. It is shown that the homoclinic spiral attractors together with the slow-fast behavior give rise to a new type of bursting activity in this system. Intervals of fast oscillations for such type of bursting alternate with slow motions of two types: small amplitude oscillations near a saddle-focus equilibrium and motions near a stable slow manifold of a fast subsystem. We demonstrate that such type of bursting activity can be either chaotic or regular.