Transient Chaos Generates Small Chimeras

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.

19 pages, 9 figure Accepted for publication in Physical Review E

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Cited by in corpus (5)

• Pattern formation and chimera states in 2D SQUID metamaterials
• Multi-branched resonances, chaos through quasiperiodicity, and asymmetric states in a superconducting dimer
• Chimera states in networks of locally and non-locally coupled SQUIDs
• Tuning of Strong Nonlinearity in rf SQUID Meta-Atoms
• Effects of Strong Capacitive Coupling Between Meta-Atoms in rf SQUID Metamaterials