55
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators

      Preprint
      ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          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.

          Related collections

          Most cited references70

          • Record: found
          • Abstract: found
          • Article: not found

          Low dimensional behavior of large systems of globally coupled oscillators.

          It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the macroscopic evolution of the systems considered. For example, an exact, closed form solution for the nonlinear time evolution of the Kuramoto problem with a Lorentzian oscillator frequency distribution function is obtained. Low dimensional behavior is also demonstrated for several prototypical extensions of the Kuramoto model, and time-delayed coupling is also considered. (c) 2008 American Institute of Physics.
            Bookmark
            • Record: found
            • Abstract: found
            • Article: not found

            Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model.

            Single-neuron recordings from behaving primates have established a link between working memory processes and information-specific neuronal persistent activity in the prefrontal cortex. Using a network model endowed with a columnar architecture and based on the physiological properties of cortical neurons and synapses, we have examined the synaptic mechanisms of selective persistent activity underlying spatial working memory in the prefrontal cortex. Our model reproduces the phenomenology of the oculomotor delayed-response experiment of Funahashi et al. (S. Funahashi, C.J. Bruce and P.S. Goldman-Rakic, Mnemonic coding of visual space in the monkey's dorsolateral prefrontal cortex. J Neurophysiol 61:331-349, 1989). To observe stable spontaneous and persistent activity, we find that recurrent synaptic excitation should be primarily mediated by NMDA receptors, and that overall recurrent synaptic interactions should be dominated by inhibition. Isodirectional tuning of adjacent pyramidal cells and interneurons can be accounted for by a structured pyramid-to-interneuron connectivity. Robust memory storage against random drift of the tuned persistent activity and against distractors (intervening stimuli during the delay period) may be enhanced by neuromodulation of recurrent synapses. Experimentally testable predictions concerning the neural basis of working memory are discussed.
              Bookmark
              • Record: found
              • Abstract: found
              • Article: not found

              The metastable brain.

              Neural ensembles oscillate across a broad range of frequencies and are transiently coupled or "bound" together when people attend to a stimulus, perceive, think, and act. This is a dynamic, self-assembling process, with parts of the brain engaging and disengaging in time. But how is it done? The theory of Coordination Dynamics proposes a mechanism called metastability, a subtle blend of integration and segregation. Tendencies for brain regions to express their individual autonomy and specialized functions (segregation, modularity) coexist with tendencies to couple and coordinate globally for multiple functions (integration). Although metastability has garnered increasing attention, it has yet to be demonstrated and treated within a fully spatiotemporal perspective. Here, we illustrate metastability in continuous neural and behavioral recordings, and we discuss theory and experiments at multiple scales, suggesting that metastable dynamics underlie the real-time coordination necessary for the brain's dynamic cognitive, behavioral, and social functions. Copyright © 2014 Elsevier Inc. All rights reserved.
                Bookmark

                Author and article information

                Journal
                2014-03-24
                2015-02-18
                Article
                10.1088/0951-7715/28/3/R67
                1403.6204
                6ddc6735-7630-45a9-b6c6-c55916bd4ba5

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                34C15, 34C23, 35B36, 82C22, 82C44
                Nonlinearity 28, R67-R87 (2015)
                26 pages, 3 figures
                nlin.CD math-ph math.MP nlin.PS

                Mathematical physics,Mathematical & Computational physics,Nonlinear & Complex systems

                Comments

                Comment on this article