A new class of chimeras in locally coupled oscillators with small-amplitude, high-frequency asynchrony and large-amplitude, low-frequency synchrony (2105.08260v2)

Abstract: Chimeras are surprising yet important states in which domains of decoherent (asynchronous) and coherent (synchronous) oscillations co-exist. In this article, we report on the discovery of a new class of chimeras, called {\it mixed-amplitude chimera states}, in which the structures, amplitudes, and frequencies of the oscillations differ substantially in the decoherent and coherent regions. These mixed-amplitude chimeras exhibit domains of decoherent small-amplitude oscillations (phase waves) coexisting with domains of stable and coherent large-amplitude or mixed-mode oscillations. They are observed in a prototypical bistable partial differential equation with spatially homogeneous kinetics and purely local, isotropic diffusion. New bifurcations are identified in which the mixed-amplitude chimeras emerge from, or are annihilated in, common large-amplitude solutions. Also, key singularities, folded nodes and folded saddles, arising commonly in multi-scale, bistable systems play important roles, and these have not previously been studied in systems with chimeras. The discovery of these mixed-amplitude chimeras is an important advance for understanding some processes in neuroscience, pattern formation, and physics which involve both small-amplitude and large-amplitude oscillations. It may also be of use for understanding some aspects of EEG recordings from animals that exhibit unihemispheric slow-wave sleep.