  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.
