Is repulsion good for the health of chimeras?

Yes! Very much so. A chimera state refers to the coexistence of a coherent-incoherent dynamical evolution of identically coupled oscillators. We investigate the impact of multiplexing of a layer having repulsively coupled oscillators on the occurrence of chimeras in the layer having attractively coupled identical oscillators. We report that there exists an enhancement in the appearance of the chimera state in one layer of the multiplex network in the presence of repulsive coupling in the other layer. Furthermore, we show that a small amount of inhibition or repulsive coupling in one layer is sufficient to yield the chimera state in another layer by destroying its synchronized behavior. These results can be used to obtain insight into dynamical behaviors of those systems where both attractive and repulsive couplings exist among their constituents.

[1]  J. Dostrovsky,et al.  High-frequency Synchronization of Neuronal Activity in the Subthalamic Nucleus of Parkinsonian Patients with Limb Tremor , 2000, The Journal of Neuroscience.

[2]  Sarika Jalan,et al.  Birth and death of chimera: Interplay of delay and multiplexing , 2016, 1610.01761.

[3]  K Lehnertz,et al.  Irregular macroscopic dynamics due to chimera states in small-world networks of pulse-coupled oscillators , 2014 .

[4]  Matjaz Perc,et al.  Chimera states: Effects of different coupling topologies , 2017, 1705.06786.

[5]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[6]  C. Laing.  Chimeras in networks with purely local coupling. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Sarika Jalan,et al.  Cluster Synchronization in Multiplex Networks , 2014 .

[8]  V. K. Chandrasekar,et al.  Chimera and globally clustered chimera: impact of time delay. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Dibakar Ghosh,et al.  Chimera states in bursting neurons. , 2015, Physical review. E.

[10]  Katharina Krischer,et al.  A classification scheme for chimera states. , 2016, Chaos.

[11]  Katharina Krischer,et al.  Clustering as a prerequisite for chimera states in globally coupled systems. , 2014, Physical review letters.

[12]  Sarika Jalan,et al.  Emergence of Chimera in Multiplex Network , 2015, Int. J. Bifurc. Chaos.

[13]  Edgar Knobloch,et al.  Multicluster and traveling chimera states in nonlocal phase-coupled oscillators. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  S. Jalan,et al.  Evolution of correlated multiplexity through stability maximization. , 2016, Physical review. E.

[15]  Dibakar Ghosh,et al.  Imperfect traveling chimera states induced by local synaptic gradient coupling. , 2016, Physical review. E.

[16]  Soumen Majhi,et al.  Chimera states in a multilayer network of coupled and uncoupled neurons. , 2017, Chaos.

[17]  S. Jalan,et al.  Extreme-value statistics of networks with inhibitory and excitatory couplings. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  L S Tsimring,et al.  Repulsive synchronization in an array of phase oscillators. , 2005, Physical review letters.

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

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

[21]  Eckehard Schöll,et al.  Synchronization patterns and chimera states in complex networks: Interplay of topology and dynamics , 2016 .

[22]  Maria V. Sanchez-Vives,et al.  Cellular and network mechanisms of slow oscillatory activity (<1 Hz) and wave propagations in a cortical network model. , 2003, Journal of neurophysiology.

[23]  Laurent Larger,et al.  Virtual chimera states for delayed-feedback systems. , 2013, Physical review letters.

[24]  S. K. Dana,et al.  Excitation and suppression of chimera states by multiplexing. , 2016, Physical review. E.

[25]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[26]  Takeo Watanabe,et al.  Night Watch in One Brain Hemisphere during Sleep Associated with the First-Night Effect in Humans , 2016, Current Biology.

[27]  A. Sen,et al.  Chimera states: the existence criteria revisited. , 2013, Physical review letters.

[28]  P. K. Roy,et al.  Chimeralike states in a network of oscillators under attractive and repulsive global coupling. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Camellia Sarkar,et al.  Multilayer network decoding versatility and trust , 2015, ArXiv.

[30]  Kaspar Anton Schindler,et al.  All together now: Analogies between chimera state collapses and epileptic seizures , 2016, Scientific Reports.

[31]  M G Cosenza,et al.  Chimeras and clusters in networks of hyperbolic chaotic oscillators. , 2017, Physical review. E.

[32]  Sarika Jalan,et al.  Emergence of clustering: role of inhibition. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Mark J Panaggio,et al.  Chimera states on the surface of a sphere. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Jürgen Kurths,et al.  The role of asymmetrical and repulsive coupling in the dynamics of two coupled van der Pol oscillators. , 2016, Chaos.

[35]  Zhigang Zheng,et al.  Chimera states on complex networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Z. Wang,et al.  The structure and dynamics of multilayer networks , 2014, Physics Reports.

[37]  G F Ayala,et al.  Genesis of epileptic interictal spikes. New knowledge of cortical feedback systems suggests a neurophysiological explanation of brief paroxysms. , 1973, Brain research.

[38]  Hopf bifurcation and multistability in a system of phase oscillators. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Philipp Hövel,et al.  When nonlocal coupling between oscillators becomes stronger: patched synchrony or multichimera states. , 2012, Physical review letters.

[40]  Soumen Majhi,et al.  Chimera states in uncoupled neurons induced by a multilayer structure , 2016, Scientific Reports.

[41]  S Yanchuk,et al.  Stationary patterns of coherence and incoherence in two-dimensional arrays of non-locally-coupled phase oscillators. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

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