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

TL;DR

This paper introduces a new class of chimeras called mixed-amplitude chimeras, where asynchronous and synchronous regions differ significantly in oscillation amplitude and frequency, advancing understanding of complex oscillatory patterns.

Contribution

The study discovers and characterizes mixed-amplitude chimera states in bistable PDEs, revealing new bifurcations and the role of singularities like folded nodes and saddles.

Findings

Mixed-amplitude chimeras coexist with small and large oscillations.

New bifurcations lead to emergence or annihilation of these chimeras.

Singularities such as folded nodes influence chimera dynamics.

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.