Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators

TL;DR

This paper investigates the emergence and complexity of chimera states in coupled phase oscillators, revealing how global feedback induces diverse regular and irregular localized excitation patterns, including chaotic behaviors.

Contribution

It introduces a global feedback mechanism linking phase lag to the order parameter, enabling the observation of chimera states in small oscillator systems and analyzing their chaotic dynamics.

Findings

Chimera states can be induced in small oscillator systems with global feedback.

Chaotic chimera states emerge via period doubling, torus breakup, and intermittency.

Localized phase slipping events form the basis of observed patterns.

Abstract

We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order parameter, we can observe chimera states also for systems with a small number of oscillators. Numerical simulations show a huge variety of regular and irregular patterns composed of localized phase slipping events of single oscillators. Using methods of classical finite dimensional chaos and bifurcation theory, we can identify the emergence of chaotic chimera states as a result of transitions to chaos via period doubling cascades, torus breakup, and intermittency. We can explain the observed phenomena by a mechanism of self-modulated excitability in a discrete excitable medium.