American Journal of Physics and Applications
Volume 7, Issue 1, January 2019, Pages: 27-33
Received: Jan. 24, 2019;
Accepted: Mar. 6, 2019;
Published: Mar. 19, 2019
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Hao Yin, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, China
The aim of this study is to investigate the chimera states in three populations of pendulum-like elements with inertia in varying network topology. Considering the coupling strength between oscillators within each population is stronger than the inter-population coupling, we search for the chimera states in three populations of pendulum-like elements under the ring and the chain structures by adjusting the inertia and the damping parameter. The numerical evidence is presented showing that chimera states exist in a narrow interval of inertia in ring and chain structures. It is found that chimera states cease to exist with the decreasing of damping parameter. Furthermore, it is revealed that there is a linear relationship between the inertia (m) and damping parameter threshold (εth) in the two network structures.
Chimera States in Three Populations of Pendulum-Like Elements with Inertia, American Journal of Physics and Applications.
Vol. 7, No. 1,
2019, pp. 27-33.
Y. Kuramoto, D. Battogtokh. Coexistence of coherence and incoherence in nonlocally coupled phase oscillators. Physics, 2002(4): 385.
D. M. Abrams, S. H. Strogatz. Chimera states for coupled oscillators. Physical Review Letters, 2004, 93(17): 174102.
D. M. Abrams. Solvable model for chimera states of coupled oscillators. Physical Review Letters, 2008, 101(8): 084103.
E. A. Martens. Bistable chimera attractors on a triangular network of oscillator populations. Physical Review E, 2010, 82(1): 016216.
E. A. Martens. Chimeras in a network of three oscillator populations with varying network topology. Chaos, 2010, 20(4): 043122.
D. M. Abrams, S. H. Strogatz. Chimera States in a ring of nonlocally coupled oscillators. International Journal of Bifurcation & Chaos, 2006, 16(01): 21-37.
C. R. Laing. The dynamics of chimera states in heterogeneous Kuramoto networks. Physica D, 2009, 238(16): 1569-1588.
O. E. Omel’chenko, M. E. Wolfrum, Y. L. Maistrenko. Chimera states as chaotic spatiotemporal patterns. Physical Review E, 2010, 81(2): 065201.
M. Wolfrum. Chimera states are chaotic transients. Physical Review E, 2011, 84(2): 015201.
M. Wolfrum, O. E. Omel’chenko, S. Yanchuk, et al. Spectral properties of chimera states. Chaos, 2011, 21(1): 910.
J. Sieber, O. E. Omel’chenko, M. Wolfrum. Controlling unstable chaos: Stabilizing chimera states by feedback. Physical Review Letters, 2014, 112(5): 054102.
S. I. Shima, Y. Kuramoto. Rotating spiral waves with phase-randomized core in nonlocally coupled oscillators. Physical Review E, 2004, 69(3): 036213.
Y. Kuramoto, S. I. Shima. Rotating spirals without phase singularity in Reaction-Diffusion systems. Progress of Theoretical Physics Supplement, 2003, 150(150): 115-125.
E. A. Martens, C. R. Laing, S. H. Strogatz. Solvable model of spiral wave chimeras. Physical Review Letters, 2010, 104(4): 044101.
O. E. Omel’chenko, M. Wolfrum, S. Yanchuk, et al. Stationary patterns of coherence and incoherence in two-dimensional arrays of non-locally-coupled phase oscillators. Physical Review E, 2012, 85(3): 036210.
M. J. Panaggio, D. M. Abrams. Chimera states on a flat torus. Physical Review Letters, 2013, 110(9): 094102.
M. J. Panaggio, D. M. Abrams. Chimera states on the surface of a sphere. Physical Review E, 2015, 91(2): 022909.
T. Bountis, V. G. Kanas, J. Hizanidis, et al. Chimera states in a two–population network of coupled pendulum–like elements. European Physical Journal Special Topics, 2014, 223(4): 721-728.
S. Olmi, E. A. Martens, S. Thutupalli, et al. Intermittent chaotic chimeras for coupled rotators. Physical Review E, 2015, 92(3): 030901.
I. V. Belykh, B. N. Brister, V. N. Belykh. Bistability of patterns of synchrony in Kuramoto oscillators with inertia. Chaos, 2016, 26(9):094822.
Y. Maistrenko, S. Brezetsky, P. Jaros, et al. The smallest chimera states. Physical Review E, 2016, 95.
Y. Zhu, Z. Zheng, J. Yang. Reversed two-cluster chimera state in non-locally coupled oscillators with heterogeneous phase lags. Europhysics Letters, 2013, 103(1): 10007.
E. A. Martens, C. Bick, M. J. Panaggio. Chimera states in two populations with heterogeneous phase-lag. Chaos, 2016, 26(9): 094819.
C. U. Choe, R. S. Kim, J. S. Ri. Chimera and modulated drift states in a ring of nonlocally coupled oscillators with heterogeneous phase lags. Physical Review E, 2017, 96(3).
E. A. Martens, E. Barreto, S. H. Strogatz, et al. Exact results for the Kuramoto model with a bimodal frequency distribution. Physical Review E, 2009, 79(2): 026204.
Y. Terada, T. Aoyagi. Dynamics of two populations of phase oscillators with different frequency distributions. Physical Review E, 2016, 94(1): 012213.