On the road towards multidimensional tori

TL;DR

This paper investigates the persistence and destruction of multi-frequency tori in coupled oscillators, revealing how adding oscillators and varying coupling affects system dynamics, including chaos and synchronization.

Contribution

It demonstrates how the addition of a third oscillator influences the stability of three-frequency tori and the emergence of four-frequency tori in driven oscillator systems.

Findings

Adding a third oscillator destroys three-frequency tori.

Four-frequency tori become dominant as coupling decreases.

Complete synchronization domains can vanish with three oscillators.

Abstract

The problem of persistence of four-frequency tori is considered in models represented by the coupled periodically driven self-oscillators. We show that the adding the third oscillator gives rise to destruction of the three-frequency tori, with appearance of regions of either chaotic attractors or four-frequency tori. As the coupling strength decreases, the four-frequency tori dominate, and the amplitude threshold of their occurrence vanishes. Also, for three oscillators, a domain of complete synchronization of the system by the external driving can disappear.