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.
5 More- Received 4 June 2019
- Revised 12 November 2019
- Accepted 21 January 2020
DOI:https://doi.org/10.1103/PhysRevX.10.011044
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Imagine you and your friend sitting on the two ends of a seesaw. When disturbed, the seesaw can switch between its two stable states. As you go up, your friend goes down, and vice versa. When the disturbances are random, the seesaw can be modeled as a noisy bistable system. Theories on stochastic transitions predict that as the level of noise decreases, the waiting time between switching events increases exponentially—you could be stuck on the ground or in the air for a very long time when noise is small. Here, we introduce a class of bistable systems for which the switching rate decreases only algebraically with noise intensity. This unexpected behavior means that the system is extremely sensitive to noise: Even a light breeze would cause the seesaw to swing up and down erratically.
We demonstrate this anomalous switching behavior for the interesting case of chimera states, which are dynamical patterns in oscillator networks exhibiting the coexistence of coherence and incoherence. In our systems, noise induces power-law switching between the coherent and incoherent portions of the chimeras. In particular, switching persists for arbitrarily small noise even though each configuration is stable in the absence of noise.
Similar power-law switching dynamics are likely to occur in other systems, potentially even biological ones. Exploitation of this effect could also lead to new ways to detect small noise in experiments.