Effects of different initial conditions on the emergence of chimera states

Abstract Chimeras are fascinating spatiotemporal states that emerge in coupled oscillators. These states are characterized by the coexistence of coherent and incoherent dynamics, and since their discovery, they have been observed in a rich variety of different systems. Here, we consider a system of non-locally coupled three-dimensional dynamical systems, which are characterized by the coexistence of fixed-points, limit cycles, and strange attractors. This coexistence creates an opportunity to study the effects of different initial conditions – from different basins of attraction – on the emergence of chimera states. By choosing initial conditions from different basins of attraction, and by varying also the coupling strength, we observe different spatiotemporal solutions, ranging from chimera states to synchronous, imperfect synchronous, and asynchronous states. We also determine conditions, in dependence on the basins of attraction, that must be met for the emergence of chimera states.

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

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

[3]  Jacques Kengne,et al.  Coexistence of Multiple Attractors and Crisis Route to Chaos in a Novel Chaotic Jerk Circuit , 2016, Int. J. Bifurc. Chaos.

[4]  Julien Clinton Sprott,et al.  An infinite 3-D quasiperiodic lattice of chaotic attractors , 2018 .

[5]  Przemyslaw Perlikowski,et al.  Multistability and Rare attractors in van der Pol-Duffing oscillator , 2011, Int. J. Bifurc. Chaos.

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

[7]  D. Abrams,et al.  Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators , 2014, 1403.6204.

[8]  Qiang Lai,et al.  Chaos, bifurcation, coexisting attractors and circuit design of a three-dimensional continuous autonomous system , 2016 .

[9]  Dibakar Ghosh,et al.  Basin stability for chimera states , 2017, Scientific Reports.

[10]  Y. Kuramoto,et al.  Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators , 2002, cond-mat/0210694.

[11]  Tomasz Kapitaniak,et al.  Chimera states on the route from coherence to rotating waves. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[14]  Julien Clinton Sprott,et al.  An infinite 2-D lattice of strange attractors , 2017 .

[15]  Przemyslaw Perlikowski,et al.  Multistability in nonlinearly coupled ring of Duffing systems , 2016 .

[16]  Qiang Lai,et al.  Various Types of Coexisting Attractors in a New 4D Autonomous Chaotic System , 2017, Int. J. Bifurc. Chaos.

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

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

[19]  S Yanchuk,et al.  Spectral properties of chimera states. , 2011, Chaos.

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

[21]  Julien Clinton Sprott,et al.  Coexistence of Point, periodic and Strange attractors , 2013, Int. J. Bifurc. Chaos.

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

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

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

[25]  Sajad Jafari,et al.  Imperfect chimeras in a ring of four-dimensional simplified Lorenz systems , 2018 .

[26]  Eduardo Sontag,et al.  Untangling the wires: A strategy to trace functional interactions in signaling and gene networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[27]  Eckehard Schöll,et al.  Chimera death: symmetry breaking in dynamical networks. , 2014, Physical review letters.

[28]  Anna Zakharova,et al.  Amplitude chimeras and chimera death in dynamical networks , 2015, 1503.03371.

[29]  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.

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

[31]  Y. Maistrenko,et al.  The smallest chimera state for coupled pendula , 2016, Scientific Reports.

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

[33]  Tomasz Kapitaniak,et al.  Multi-headed chimera states in coupled pendula , 2015 .

[34]  Fatihcan M Atay,et al.  Clustered chimera states in delay-coupled oscillator systems. , 2008, Physical review letters.