Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
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TLDR
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.Abstract:
A chimera state is a spatio-temporal pattern in a network of identical coupled oscillators in which synchronous and asynchronous oscillation coexist. This state of broken symmetry, which usually coexists with a stable spatially symmetric state, has intrigued the nonlinear dynamics community since its discovery in the early 2000s. Recent experiments have led to increasing interest in the origin and dynamics of these states. Here we review the history of research on chimera states and highlight major advances in understanding their behaviour.read more
Citations
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The Kuramoto model in complex networks
Francisco A. Rodrigues,Thomas K. Dm. Peron,Thomas K. Dm. Peron,Peng Ji,Peng Ji,Jürgen Kurths +5 more
TL;DR: In this article, B. Sonnenschein, E.R. dos Santos, P.J. Schultz, C.A. Ha, M.K. Choi and C.P.
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Hidden attractors in dynamical systems
Dawid Dudkowski,Sajad Jafari,Tomasz Kapitaniak,Nikolay Kuznetsov,Nikolay Kuznetsov,Gennady A. Leonov,Awadhesh Prasad +6 more
TL;DR: In this paper, the authors discuss the most representative examples of hidden attractors, discuss their theoretical properties and experimental observations, and also describe numerical methods which allow identification of the hidden attractor.
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Chimera states in neuronal networks: A review.
TL;DR: Chimera states have attracted ample attention of researchers that work at the interface of physics and life sciences as discussed by the authors, focusing on the relevance of different synaptic connections, and on the effects of different network structures and coupling setups.
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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.
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Synchronization patterns and chimera states in complex networks: Interplay of topology and dynamics
TL;DR: In this article, a plethora of novel chimera patterns arise if one goes beyond the Kuramoto phase oscillator model, which consist of coexisting spatial domains of coherent and incoherent dynamics in networks of identical oscillators.
References
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From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators
TL;DR: In this article, the authors review 25 years of research on the Kuramoto model, highlighting the false turns as well as the successes, but mainly following the trail leading from Kuramoto's work to Crawford's recent contributions.
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Biological rhythms and the behavior of populations of coupled oscillators
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