Time-delayed feedback control of coherence resonance chimeras.

Using the model of a FitzHugh-Nagumo system in the excitable regime, we investigate the influence of time-delayed feedback on noise-induced chimera states in a network with nonlocal coupling, i.e., coherence resonance chimeras. It is shown that time-delayed feedback allows for the control of the range of parameter values where these chimera states occur. Moreover, for the feedback delay close to the intrinsic period of the system, we find a novel regime which we call period-two coherence resonance chimera.

[1]  Yuri Maistrenko,et al.  Delayed-feedback chimera states: Forced multiclusters and stochastic resonance , 2015, 1511.03634.

[2]  L Schimansky-Geier,et al.  Coherence resonance near a Hopf bifurcation. , 2005, Physical review letters.

[3]  Fatihcan M. Atay,et al.  Complex Time-Delay Systems , 2010 .

[4]  Eckehard Schöll,et al.  Coherence-Resonance Chimeras in a Network of Excitable Elements. , 2015, Physical review letters.

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

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

[7]  Eckehard Schöll,et al.  Time-delayed feedback control of coherence resonance near subcritical Hopf bifurcation: theory versus experiment. , 2014, Chaos.

[8]  Eckehard Schöll,et al.  Amplitude-phase coupling drives chimera states in globally coupled laser networks. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Eckehard Schöll,et al.  Delay-Induced Multistability Near a Global bifurcation , 2008, Int. J. Bifurc. Chaos.

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

[11]  Eckehard Schöll,et al.  Modulating coherence resonance in non-excitable systems by time-delayed feedback , 2014, 1410.1686.

[12]  E Schöll,et al.  Control of unstable steady states by time-delayed feedback methods. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Michael Schanz,et al.  Synergetic System Analysis for the Delay-Induced Hopf Bifurcation in the Wright Equation , 2002, SIAM J. Appl. Dyn. Syst..

[14]  V. K. Chandrasekar,et al.  Globally clustered chimera states in delay-coupled populations. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  MacDonald,et al.  Two-dimensional vortex lattice melting. , 1993, Physical review letters.

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

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

[18]  Alexander B. Neiman,et al.  COHERENCE RESONANCE AT NOISY PRECURSORS OF BIFURCATIONS IN NONLINEAR DYNAMICAL SYSTEMS , 1997 .

[19]  Laurent Larger,et al.  Laser chimeras as a paradigm for multistable patterns in complex systems , 2014, Nature Communications.

[20]  J. García-Ojalvo,et al.  Effects of noise in excitable systems , 2004 .

[21]  J Kurths,et al.  Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[23]  J. Kurths,et al.  Coherence Resonance in a Noise-Driven Excitable System , 1997 .

[24]  Kestutis Pyragas Continuous control of chaos by self-controlling feedback , 1992 .

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

[26]  E Schöll,et al.  Delayed feedback as a means of control of noise-induced motion. , 2003, Physical review letters.

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

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

[29]  Philipp Hövel,et al.  Delay control of coherence resonance in type-I excitable dynamics , 2010 .

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

[31]  Zonghua Liu,et al.  Robust features of chimera states and the implementation of alternating chimera states , 2010 .

[32]  T. Vadivasova,et al.  Coherence resonance and stochastic synchronization in a nonlinear circuit near a subcritical Hopf bifurcation , 2013 .

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

[34]  Eckehard Schöll,et al.  Chimera patterns under the impact of noise. , 2015, Physical review. E.