Cascades of Multi-headed Chimera States for Coupled Phase Oscillators
TL;DR: In this article, the authors studied the appearance of chimera states in networks of phase oscillators with attractive and repulsive interactions, i.e., when the coupling respectively favors synchronization or works against it.
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Abstract: Chimera state is a recently discovered dynamical phenomenon in arrays of nonlocally coupled oscillators, that displays a self-organized spatial pattern of co-existing coherence and incoherence. We discuss the appearance of the chimera states in networks of phase oscillators with attractive and with repulsive interactions, i.e. when the coupling respectively favors synchronization or works against it. By systematically analyzing the dependence of the spatiotemporal dynamics on the level of coupling attractivity/repulsivity and the range of coupling, we uncover that different types of chimera states exist in wide domains of the parameter space as cascades of the states with increasing number of intervals of irregularity, so-called chimera's heads. We report three scenarios for the chimera birth: 1) via saddle-node bifurcation on a resonant invariant circle, also known as SNIC or SNIPER, 2) via blue-sky catastrophe, when two periodic orbits, stable and saddle, approach each other creating a saddle-node periodic orbit, and 3) via homoclinic transition with complex multistable dynamics including an "eight-like" limit cycle resulting eventually in a chimera state.
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Citations
Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
TL;DR: A review of the history of research on chimera states and major advances in understanding their behavior can be found in this article, where the authors highlight major advances on understanding their behaviour.
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Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience
TL;DR: In this article, a set of mathematical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical framework for further successful applications of mathematics to understand network dynamics in neuroscience.
Robustness of chimera states for coupled FitzHugh-Nagumo oscillators.
TL;DR: It is shown that modifications of coupling topologies cause qualitative changes of chimera states: additional random links induce a shift of the stability regions in the system parameter plane, and gaps in the connectivity matrix result in a change of the multiplicity of incoherent regions of the chimera state.
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Laser chimeras as a paradigm for multistable patterns in complex systems
TL;DR: A powerful and highly controllable experiment based on an optoelectronic delayed feedback applied to a wavelength tuneable semiconductor laser, with which a wide variety of chimera patterns can be accurately investigated and interpreted, and a cascade of higher-order chimeras as a pattern transition from N to N+1 clusters of chaoticity is uncovered.
The mathematics behind chimera states
Abstract: Chimera states are self-organized spatiotemporal patterns of coexisting coherence and incoherence. We give an overview of the main mathematical methods used in studies of chimera states, focusing on chimera states in spatially extended coupled oscillator systems. We discuss the continuum limit approach to these states, Ott-Antonsen manifold reduction, finite size chimera states, control of chimera states and the influence of system design on the type of chimera state that is observed.
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References
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Chimera and phase-cluster states in populations of coupled chemical oscillators
TL;DR: In this article, an experimental demonstration of these states in a network of discrete chemical oscillators reveals behaviour that differs from that predicted by existing phase-oscillator models, and they are used to describe the stable coexistence of synchronous and incoherent dynamics.
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Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators
TL;DR: In this article, the phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling, and peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into two domains, one composed of mutually synchronized oscillators with unique frequency and the other composed of desynchronized oscillators having distributed frequencies.
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Chimera states in mechanical oscillator networks
TL;DR: A simple experiment with mechanical oscillators coupled in a hierarchical network is devised to show that chimeras emerge naturally from a competition between two antagonistic synchronization patterns, and a mathematical model shows that the self-organization observed is controlled by elementary dynamical equations from mechanics that are ubiquitous in many natural and technological systems.
Solvable model for chimera states of coupled oscillators
TL;DR: The first exact results about the stability, dynamics, and bifurcations of chimera states are obtained by analyzing a minimal model consisting of two interacting populations of oscillators.