Abstract
We report on a new type of chimera state that attracts almost all initial conditions and exhibits power-law switching behavior in networks of coupled oscillators. Such switching chimeras consist of two symmetric configurations, which we refer to as subchimeras, in which one cluster is synchronized and the other is incoherent. Despite each subchimera being linearly stable, switching chimeras are extremely sensitive to noise: arbitrarily small noise triggers and sustains persistent switching between the two symmetric subchimeras. The average switching frequency scales as a power law with the noise intensity, which is in contrast with the exponential scaling observed in typical stochastic transitions. Rigorous numerical analysis reveals that the power-law switching behavior originates from intermingled basins of attraction associated with the two subchimeras, which in turn are induced by chaos and symmetry in the system. The theoretical results are supported by experiments on coupled optoelectronic oscillators, which demonstrate the generality and robustness of switching chimeras.
Highlights
The relationship between symmetry and synchronization underlies many recent discoveries in network dynamics
A switching chimera can be seen as a chimera state whose symmetry is not broken when considering the longterm dynamics—asymptotically, one cannot distinguish between the behavior of the two clusters
The theoretical, computational, and experimental results presented here offer a comprehensive characterization of a novel class of chimera states that are globally attractive and exhibit power-law switching dynamics
Summary
The relationship between symmetry and synchronization underlies many recent discoveries in network dynamics. We report on switching chimeras, which are chimera states that both exhibit power-law dependence of the switching frequency on noise intensity and attract almost all initial conditions in the absence of control. The power-law switching dynamics is a signature of critical behavior and stems from a vanishing quasipotential barrier between the two metastable states. It follows that the switching persists indefinitely for any nonzero noise intensity. For any nonzero noise intensity, the long-term dynamical symmetry is restored due to the persistent switching between the two subchimeras.
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