Quasi-periodic oscillations in a network of four Rossler chaotic oscillators

TL;DR

This paper investigates the emergence of multi-frequency invariant tori in a network of four non-identical Rossler chaotic oscillators, revealing complex bifurcation phenomena such as quasi-periodic Hopf and saddle-node bifurcations.

Contribution

It demonstrates the conditions under which multi-frequency tori appear in a small network of chaotic oscillators, highlighting new bifurcation pathways.

Findings

Existence of two-, three-, and four-frequency invariant tori

Identification of secondary quasi-periodic Hopf bifurcations

Discovery of saddle-node homoclinic bifurcations of tori

Abstract

We consider a network of four non-identical chaotic Rossler oscillators. The possibility is shown of appearance of two-, three- and four-frequency invariant tori resulting from secondary quasi-periodic Hopf bifurcations and saddle-node homoclinic bifurcations of tori.