Critical Behavior at the Onset of Multichimera States in a Coupled-Oscillator Array

TL;DR

This study numerically explores the critical transition to multichimera states in coupled oscillators, revealing unique power-law behaviors and a new class of non-equilibrium phase transition driven by traveling waves.

Contribution

It identifies a novel non-equilibrium critical phenomenon in coupled oscillators, characterized by unique critical exponents and the role of traveling waves in multichimera state formation.

Findings

Power-law scaling of asynchronous site fraction near criticality

Distinct critical exponents from known phase transitions

Traveling waves facilitate non-local interactions in multichimera states

Abstract

We numerically investigate the onset of multi-chimera states in a linear array of coupled oscillators. As the phase delay $\alpha$ is increased, they exhibit a continuous transition from the globally synchronized state to the multichimera state consisting of asynchronous and synchronous domains. Large-scale simulations show that the fraction of asynchronous sites $\rho_a$ obeys the power law $\rho_a \sim (\alpha - \alpha_c)^{\beta_a}$, and that the spatio-temporal gaps between asynchronous sites show power-law distributions at the critical point. The critical exponents are distinct from those of the (1+1)-dimensional directed percolation and other absorbing-state phase transitions, indicating that this transition belongs to a new class of non-equilibrium critical phenomena. Crucial roles are played by traveling waves that rejuvenate asynchronous clusters by mediating non-local interactions between them.