Chimera state and route to explosive synchronization

Abstract Transition to explosive synchronization is exhibited in networks of Kuramoto oscillators with a positive correlation between the oscillator dynamics and their inner topological structure encoded in the vertex degrees relations, shedding a light over the explosive critical phenomena. Here we study emergence of chimera states for the large amplitude oscillations when degree-frequency correlation is established only for the vertices with the highest degrees. For the strong coupling regime no simultaneous coexistence of coherence and incoherence signatures is observed. The connection between the network dynamics and the range and strength of coupling is elucidated through extensive analytical investigation, presenting realistic simulations of a scale-free neural network of Caenorhabditis elegans.

[1]  A. Panfilov,et al.  Spiral breakup as a model of ventricular fibrillation. , 1998, Chaos.

[2]  M. Newman,et al.  Finding community structure in networks using the eigenvectors of matrices. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[4]  S. Strogatz.  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators , 2000 .

[5]  Xin Hu,et al.  Exact solution for first-order synchronization transition in a generalized Kuramoto model , 2014, Scientific Reports.

[6]  E. Ott,et al.  Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  M. A. Muñoz,et al.  Journal of Statistical Mechanics: An IOP and SISSA journal Theory and Experiment Detecting network communities: a new systematic and efficient algorithm , 2004 .

[8]  E. Witten.  Supersymmetry and Morse theory , 1982 .

[9]  Michael Menzinger,et al.  Clustering and the synchronization of oscillator networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  R. E. Amritkar,et al.  Self-organized and driven phase synchronization in coupled maps. , 2002, Physical review letters.

[11]  R. Roy,et al.  Experimental observation of chimeras in coupled-map lattices , 2012, Nature Physics.

[12]  W. Baxter,et al.  Stationary and drifting spiral waves of excitation in isolated cardiac muscle , 1992, Nature.

[13]  E. Ott,et al.  Long time evolution of phase oscillator systems. , 2009, Chaos.

[14]  Tore Opsahl,et al.  Clustering in weighted networks , 2009, Soc. Networks.

[15]  N. Lazarides,et al.  Chimeras in SQUID metamaterials , 2014, 1408.6072.

[16]  Francesco Sorrentino,et al.  Cluster synchronization and isolated desynchronization in complex networks with symmetries , 2013, Nature Communications.

[17]  Matjaz Perc,et al.  Amplification of information transfer in excitable systems that reside in a steady state near a bifurcation point to complex oscillatory behavior. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  K. Showalter,et al.  Chimera and phase-cluster states in populations of coupled chemical oscillators , 2012, Nature Physics.

[19]  S. Strogatz,et al.  Solvable model for chimera states of coupled oscillators. , 2008, Physical review letters.

[20]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  S. Strogatz,et al.  Chimera states for coupled oscillators. , 2004, Physical review letters.

[22]  Mattia Frasca,et al.  Chimera states in time-varying complex networks. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[24]  S. L. Lima,et al.  Behavioral, neurophysiological and evolutionary perspectives on unihemispheric sleep , 2000, Neuroscience & Biobehavioral Reviews.

[25]  A. Mikhailov,et al.  Mutual synchronization and clustering in randomly coupled chaotic dynamical networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Guanrong Chen,et al.  Synchronous Bursts on Scale-Free Neuronal Networks with Attractive and Repulsive Coupling , 2010, PloS one.

[27]  Sergio Gómez,et al.  Explosive synchronization transitions in scale-free networks. , 2011, Physical review letters.