Basins of Attraction for Chimera States

Abstract

Chimera states---curious symmetry-broken states in systems of identical coupled oscillators---typically occur only for certain initial conditions. Here we analyze their basins of attraction in a simple system comprised of two populations. Using perturbative analysis and numerical simulation we evaluate asymptotic states and associated destination maps, and demonstrate that basins form a complex twisting structure in phase space. Understanding the basins' precise nature may help in the development of control methods to switch between chimera patterns, with possible technological and neural system applications.

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• Chimera states in two populations with heterogeneous phase-lag
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• The changing notion of chimera states, a critical review
• Potentials and Limits to Basin Stability Estimation
• Mechanism for Strong Chimeras
• Optimal self-induced stochastic resonance in multiplex neural networks: electrical versus chemical synapses
• Critical Switching in Globally Attractive Chimeras
• A model bridging chimera state and explosive synchronization
• Stable amplitude chimera states in a network of locally coupled Stuart-Landau oscillators
• Transitions from chimeras to coherence: An analytical approach by means of the coherent stability function
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• Threefold way to the dimension reduction of dynamics on networks: an application to synchronization
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• Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators
• Chimera-like states in two distinct groups of identical populations of coupled Stuart-Landau oscillators
• Attracting Poisson Chimeras in Two-population Networks
• Mobility-induced persistent chimera states
• Identification of single- and double-well coherence-incoherence patterns by the binary distance matrix
• Coupled Moebius Maps as a Tool to Model Kuramoto Phase Synchronization
• Chimera states in multi-strain epidemic models with temporary immunity
• Chimera-like States in Structured Heterogeneous Networks
• Solitary synchronization waves in distributed oscillators populations
• Discordant synchronization patterns on directed networks of identical phase oscillators with attractive and repulsive couplings
• Frequency Synchronization Induced by Frequency Detuning
• Birth and destruction of collective oscillations in a network of two populations of coupled type 1 neurons
• Exponentially long transient time to synchronization of coupled chaotic circle maps in dense random networks
• Basins of Attraction: A Dynamical Zoo
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• Chimera and anticoordination states in learning dynamics
• Metastability of multi-population Kuramoto-Sakaguchi oscillators