Transient Chaos Generates Small Chimeras

TL;DR

This paper reveals that small chimera states in a SQUID array are generated through transient chaos, with detailed analysis of their bifurcations, basins of attraction, and underlying chaotic dynamics.

Contribution

It provides the first detailed demonstration that small chimeras arise from transient chaos and offers analytic expressions and bifurcation analysis for these states.

Findings

Small chimeras are born through transient chaos.

Basin of attraction has both ordered and fractal parts.

Transient chaos causes erratic flux oscillations and exponential escape times.

Abstract

While the chimera states themselves are usually believed to be chaotic transients, the involvement of chaos behind their self-organization is not properly distinguished or studied. In this work, we demonstrate that small chimeras in the local flux dynamics of an array of magnetically coupled superconducting quantum interference devices (SQUIDs) driven by an external field are born through transiently chaotic dynamics. We deduce analytic expressions for small chimeras and synchronous states which correspond to nonchaotic attractors in the model. We also numerically study the bifurcations underlying the multistability responsible for their generation. Transient chaos manifests itself in the short term flux oscillations with erratically fluctuating amplitudes, exponential escape time distribution and irregular dependence of the escape time to initial conditions. We classify the small chimera states in terms of the position of the non-synchronized member and numerically construct their basin of attraction. The basin is shown to possess an interesting structure consisting of both ordered and fractal parts, which again can be attributed to transient chaos.