Chimera states in coupled logistic maps with additional weak nonlocal topology.

We demonstrate the occurrence of coexisting domains of partially coherent and incoherent patterns or simply known as chimera states in a network of globally coupled logistic maps upon addition of weak nonlocal topology. We find that the chimera states survive even after we disconnect nonlocal connections of some of the nodes in the network. Also, we show that the chimera states exist when we introduce symmetric gaps in the nonlocal coupling between predetermined nodes. We ascertain our results, for the existence of chimera states, by carrying out the recurrence quantification analysis and by computing the strength of incoherence. We extend our analysis for the case of small-world networks of coupled logistic maps and found the emergence of chimeralike states under the influence of weak nonlocal topology.

[1]  N. Marwan,et al.  Introduction to focus issue: Recurrence quantification analysis for understanding complex systems. , 2018, Chaos.

[2]  Soumen Majhi,et al.  Alternating chimeras in networks of ephaptically coupled bursting neurons. , 2018, Chaos.

[3]  C. Grebogi,et al.  Riddling: Chimera's dilemma. , 2018, Chaos.

[4]  P. Hövel,et al.  Robustness of chimera states in nonlocally coupled networks of nonidentical logistic maps. , 2018, Physical review. E.

[5]  V. Anishchenko,et al.  Chimera states and intermittency in an ensemble of nonlocally coupled Lorenz systems. , 2018, Chaos.

[6]  Jinghua Xiao,et al.  Stable amplitude chimera states and chimera death in repulsively coupled chaotic oscillators , 2018 .

[7]  K. Showalter,et al.  Spiral wave chimera states in large populations of coupled chemical oscillators , 2017 .

[8]  A. V. Cano,et al.  Asymmetric cluster and chimera dynamics in globally coupled systems. , 2017, Chaos.

[9]  V. Anishchenko,et al.  Temporal intermittency and the lifetime of chimera states in ensembles of nonlocally coupled chaotic oscillators. , 2017, Chaos.

[10]  A. Politi,et al.  Collective dynamics out of thermodynamic equilibrium. , 2017, Physical review. E.

[11]  Eckehard Schöll,et al.  Mechanisms of appearance of amplitude and phase chimera states in ensembles of nonlocally coupled chaotic systems , 2017, Commun. Nonlinear Sci. Numer. Simul..

[12]  Tomasz Kapitaniak,et al.  Occurrence and stability of chimera states in coupled externally excited oscillators. , 2016, Chaos.

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

[14]  T. E. Vadivasova,et al.  Correlation analysis of the coherence-incoherence transition in a ring of nonlocally coupled logistic maps. , 2016, Chaos.

[15]  F. S. Borges,et al.  Chimera-like states in a neuronal network model of the cat brain , 2016, 1609.01534.

[16]  E. Schöll,et al.  Chimera patterns induced by distance-dependent power-law coupling in ecological networks. , 2016, Physical review. E.

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

[18]  Ramakrishna Ramaswamy,et al.  Phase oscillators in modular networks: The effect of nonlocal coupling. , 2016, Physical review. E.

[19]  J. D. Szezech,et al.  Recurrence quantification analysis of chimera states , 2015 .

[20]  Nadezhda Semenova,et al.  Does hyperbolicity impede emergence of chimera states in networks of nonlocally coupled chaotic oscillators? , 2015, 1509.05817.

[21]  Zi-Gang Huang,et al.  Emergence of multicluster chimera states , 2015, Scientific Reports.

[22]  Krishnamurthy Murali,et al.  Chimera States in Star Networks , 2015, Int. J. Bifurc. Chaos.

[23]  K. Okuda,et al.  Persistent chimera states in nonlocally coupled phase oscillators. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Hans Dierckx,et al.  Spiral wave chimeras in locally coupled oscillator systems. , 2015, Physical review. E.

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

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

[27]  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.

[28]  Kunihiko Kaneko,et al.  From globally coupled maps to complex-systems biology. , 2015, Chaos.

[29]  Philipp Hövel,et al.  Nonlinearity of local dynamics promotes multi-chimeras. , 2015, Chaos.

[30]  Philipp Hövel,et al.  Robustness of chimera states for coupled FitzHugh-Nagumo oscillators. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Y. Maistrenko,et al.  Imperfect chimera states for coupled pendula , 2014, Scientific Reports.

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

[33]  Tomasz Kapitaniak,et al.  Different types of chimera states: an interplay between spatial and dynamical chaos. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  V. K. Chandrasekar,et al.  Mechanism for intensity-induced chimera states in globally coupled oscillators. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  V. K. Chandrasekar,et al.  Observation and characterization of chimera states in coupled dynamical systems with nonlocal coupling. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  M. Rosenblum,et al.  Chimeralike states in an ensemble of globally coupled oscillators. , 2014, Physical review letters.

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

[38]  Katharina Krischer,et al.  Coexistence of synchrony and incoherence in oscillatory media under nonlinear global coupling. , 2013, Chaos.

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

[40]  Kenneth Showalter,et al.  Chimera States in populations of nonlocally coupled chemical oscillators. , 2013, Physical review letters.

[41]  Abhijit Sen,et al.  Amplitude-mediated chimera states. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  O. Hallatschek,et al.  Chimera states in mechanical oscillator networks , 2013, Proceedings of the National Academy of Sciences.

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

[44]  Simona Olmi,et al.  Collective dynamics in sparse networks. , 2012, Physical review letters.

[45]  Philipp Hövel,et al.  Transition from spatial coherence to incoherence in coupled chaotic systems. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  Carlo R. Laing,et al.  Fronts and bumps in spatially extended Kuramoto networks , 2011 .

[47]  Eckehard Olbrich,et al.  The multiple time scales of sleep dynamics as a challenge for modelling the sleeping brain , 2011, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[48]  Junzhong Yang,et al.  The oscillating two-cluster chimera state in non-locally coupled phase oscillators , 2011, 1109.4235.

[49]  Xiaoqin Luo,et al.  Effects of adaptive coupling on stochastic resonance of small-world networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[50]  Matthias Wolfrum,et al.  Chimera states are chaotic transients. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  Hanqing Wang,et al.  Synchronization and chimera states of frequency-weighted Kuramoto-oscillator networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  P. Hövel,et al.  Loss of coherence in dynamical networks: spatial chaos and chimera states. , 2011, Physical review letters.

[53]  Matthias Wolfrum,et al.  Chimera states as chaotic spatiotemporal patterns. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[55]  Arkady Pikovsky,et al.  Self-emerging and turbulent chimeras in oscillator chains. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[56]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[57]  T. Tlusty,et al.  Development of input connections in neural cultures , 2008, Proceedings of the National Academy of Sciences.

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

[59]  G Bard Ermentrout,et al.  Partially locked states in coupled oscillators due to inhomogeneous coupling. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  Peter A Tass,et al.  Chimera states: the natural link between coherence and incoherence. , 2008, Physical review letters.

[61]  G. Filatrella,et al.  Analysis of a power grid using a Kuramoto-like model , 2007, 0705.1305.

[62]  Yoji Kawamura.  Chimera Ising walls in forced nonlocally coupled oscillators. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[63]  S. Strogatz,et al.  Chimera States in a Ring of Nonlocally Coupled oscillators , 2005, Int. J. Bifurc. Chaos.

[64]  Chunguang Li,et al.  Phase synchronization in small-world networks of chaotic oscillators , 2004 .

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

[66]  C. Anteneodo,et al.  Chaos synchronization in long-range coupled map lattices , 2004, nlin/0401034.

[67]  F. Atay,et al.  Delays, connection topology, and synchronization of coupled chaotic maps. , 2003, Physical review letters.

[68]  Yoshiki Kuramoto,et al.  Rotating spiral waves with phase-randomized core in nonlocally coupled oscillators. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[69]  C. Anteneodo,et al.  Analytical results for coupled-map lattices with long-range interactions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[70]  R. E. Amritkar,et al.  Synchronized clusters in coupled map networks. I. Numerical studies. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[72]  F. Ginelli,et al.  Emergence of chaotic behaviour in linearly stable systems , 2001, nlin/0102005.

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

[74]  Gade,et al.  Synchronous chaos in coupled map lattices with small-world interactions , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[75]  W. Ditto,et al.  Computing with distributed chaos. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[76]  M. Newman,et al.  Renormalization Group Analysis of the Small-World Network Model , 1999, cond-mat/9903357.

[77]  Christian Beck,et al.  Hierarchical coupled map lattices as cascade models for hydrodynamical turbulence , 1999 .

[78]  Yoshiki Kuramoto,et al.  Multiaffine chemical turbulence , 1998 .

[79]  William L. Ditto,et al.  DYNAMICS BASED COMPUTATION , 1998 .

[80]  Mingzhou Ding,et al.  STABILITY OF SYNCHRONOUS CHAOS AND ON-OFF INTERMITTENCY IN COUPLED MAP LATTICES , 1997 .

[81]  M. Hallett,et al.  Event-related coherence and event-related desynchronization/synchronization in the 10 Hz and 20 Hz EEG during self-paced movements. , 1997, Electroencephalography and clinical neurophysiology.

[82]  Gade,et al.  Synchronization of oscillators with random nonlocal connectivity. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[83]  M. Laine,et al.  Event-related EEG desynchronization and synchronization during an auditory memory task. , 1996, Electroencephalography and clinical neurophysiology.

[84]  G. Pfurtscheller,et al.  Event-related synchronization of mu rhythm in the EEG over the cortical hand area in man , 1994, Neuroscience Letters.

[85]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[86]  Y. Kuramoto,et al.  A Soluble Active Rotater Model Showing Phase Transitions via Mutual Entertainment , 1986 .

[87]  Jacqueline McGlade,et al.  A coupled map lattice model of the growth of plant monocultures , 1996 .

[88]  H. Aref.  INTEGRABLE, CHAOTIC, AND TURBULENT VORTEX MOTION IN TWO-DIMENSIONAL FLOWS , 1983 .

[89]  M. P. Joy,et al.  F Ur Mathematik in Den Naturwissenschaften Leipzig Spectral Properties and Synchronization in Coupled Map Lattices Spectral Properties and Synchronization in Coupled Map Lattices , 2022 .