Reversed two-cluster chimera state in non-locally coupled oscillators with heterogeneous phase lags

The dynamics of non-locally coupled two-segment phase oscillators with different phase lags are investigated. It is found that there exists a reversed two-cluster chimera state if the Kuramoto oscillators possess heterogeneous phase lags. It is interesting that the frequencies of oscillators in different synchronized clusters we observed here are different and their directions of rotation are reversed. The size of clusters depends only on the phase lag. Our results can be analytically predicted and reproduced with the help of the Ott-Antonsen Ansatz.

[1]  E. Ryabov,et al.  Intramolecular vibrational redistribution: from high-resolution spectra to real-time dynamics , 2012 .

[2]  Steven H. Strogatz,et al.  Erratum: Solvable Model for Chimera States of Coupled Oscillators [Phys. Rev. Lett. 101, 084103 (2008)] , 2008 .

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

[4]  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.

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

[6]  Y. Kuramoto,et al.  Complex Ginzburg-Landau equation with nonlocal coupling. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[8]  M. Rosenblum,et al.  Partially integrable dynamics of hierarchical populations of coupled oscillators. , 2008, Physical review letters.

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

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

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

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

[13]  E. Ott,et al.  Low dimensional behavior of large systems of globally coupled oscillators. , 2008, Chaos.

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

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

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

[17]  Erik A Martens,et al.  Solvable model of spiral wave chimeras. , 2009, Physical review letters.

[18]  Carlo R Laing,et al.  Chimera states in heterogeneous networks. , 2008, Chaos.

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

[20]  Baowen Li,et al.  Thermal diode: rectification of heat flux. , 2004, Physical review letters.

[21]  Hyunsuk Hong,et al.  Kuramoto model of coupled oscillators with positive and negative coupling parameters: an example of conformist and contrarian oscillators. , 2011, Physical review letters.

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

[23]  Dwight Barkley,et al.  Computational study of turbulent laminar patterns in couette flow. , 2005, Physical review letters.