The smallest chimera states

TL;DR

This paper shows that chimera states, previously thought to require large networks, can actually occur in very small networks of just three identical oscillators with all-to-all coupling, revealing new insights into their fundamental nature.

Contribution

It demonstrates the existence of chimera states in minimal networks of three oscillators and characterizes their types and bifurcations, expanding understanding of these phenomena.

Findings

Chimera states observed in three-oscillator networks.

Identification of three types of chimera states with different behaviors.

Bifurcation analysis and parameter regions mapped as Arnold tongues.

Abstract

We demonstrate that chimera behavior can be observed in small networks consisting of three identical oscillators, with mutual all-to-all coupling. Three different types of chimeras, characterized by the coexistence of two coherent oscillators and one incoherent oscillator (i.e. rotating with another frequency) have been identified, where the oscillators show periodic (two types) and chaotic (one type) behaviors. Typical bifurcations at the transitions from full synchronization to chimera states and between different types of chimeras have been described. Parameter regions for the chimera states are obtained in the form of Arnold tongues, issued from a singular parameter point. Our analysis suggests that chimera states can be observed in small networks, relevant to various real-world systems.