About Landau-Hopf scenario in a system of coupled self-oscillators

TL;DR

This paper investigates the Landau-Hopf scenario in a network of five coupled oscillators, demonstrating how multi-frequency quasi-periodic motions emerge through bifurcations, with a proposed model illustrating these dynamics.

Contribution

It introduces a specific model of coupled oscillators to analyze the Landau-Hopf scenario and illustrates the successive emergence of higher-dimensional tori via bifurcations.

Findings

Successive birth of multi-frequency tori observed

Quasi-periodic Hopf bifurcations demonstrated

Model shows controlled activation leads to complex dynamics

Abstract

The conditions are discussed for which an ensemble of interacting oscillators may demonstrate the Landau-Hopf scenario of successive birth of multi-frequency quasi-periodic motions. A model is proposed that is a network of five globally coupled oscillators characterized by controlled degree of activation of individual oscillators. Illustrations are given for successive birth of tori of increasing dimension via quasi-periodic Hopf bifurcations.