Riddling: Chimera's dilemma

Abstract

We investigate the basin of attraction properties and its boundaries for chimera states in a circulant network of Hénon maps. Chimera states, for which coherent and incoherent domains coexist, emerge as a consequence of the coexistence of basin of attractions for each state. It is known that the coexisting basins of attraction lead to a hysteretic behaviour in the diagrams for the density of incoherent and coherent states as a function of a varying parameter. Consequently, the distribution of chimera states can remain invariant by a parameter change, as well as it can suffer subtle changes when one of the basin ceases to exist. A similar phenomenon is observed when perturbations are applied in the initial conditions. By means of the uncertainty exponent, we characterise the basin boundaries between the coherent and chimera states, and between the incoherent and chimera states, and uncover fractal and riddled boundaries, respectively. This way, we show that the density of chimera states can be not only moderately sensitive but also highly sensitive to initial conditions. This chimera's dilemma is a consequence of the fractal and riddled nature of the basins boundaries.

Published

References in corpus (12)

• Chimera States for Coupled Oscillators
• Chimera States in Mechanical Oscillator Networks
• Solvable model for chimera states of coupled oscillators
• Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators
• Loss of coherence in dynamical networks: spatial chaos and chimera states
• Transition from spatial coherence to incoherence in coupled chaotic systems
• Observation and characterization of chimera states in coupled dynamical systems with nonlocal coupling
• Basin stability for chimera states
• Chimera in a neuronal network model of the cat brain
• Basins of Attraction for Chimera States
• Hyperbolicity impedes emergence of chimera states in networks of nonlocally coupled chaotic oscillators
• Potentials and Limits to Basin Stability Estimation

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• Transition from chimera/solitary states to traveling waves
• Identification of single- and double-well coherence-incoherence patterns by the binary distance matrix
• Chimera states for a globally coupled sine circle map lattice: spatiotemporal intermittency and hyperchaos