|
|
|
Entangled chimeras in nonlocally coupled bicomponent phase oscillators: From synchronous to asynchronous chimeras |
Qiong-Lin Dai1, Xiao-Xuan Liu1, Kai Yang1, Hong-Yan Cheng1, Hai-Hong Li1, Fagen Xie2( ), Jun-Zhong Yang1() |
1. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
2. Department of Research and Evaluation, Kaiser Permanente Southern California, Pasadena, CA 91101, USA |
|
|
|
|
Abstract Chimera states, a symmetry-breaking spatiotemporal pattern in nonlocally coupled identical dynamical units, have been identified in various systems and generalized to coupled nonidentical oscillators. It has been shown that strong heterogeneity in the frequencies of nonidentical oscillators might be harmful to chimera states. In this work, we consider a ring of nonlocally coupled bicomponent phase oscillators in which two types of oscillators are randomly distributed along the ring: some oscillators with natural frequency ω1 and others with ω2 . In this model, the heterogeneity in frequency is measured by frequency mismatch |ω1−ω2| between the oscillators in these two subpopulations. We report that the nonlocally coupled bicomponent phase oscillators allow for chimera states no matter how large the frequency mismatch is. The bicomponent oscillators are composed of two chimera states, one supported by oscillators with natural frequency ω1 and the other by oscillators with natural frequency ω2. The two chimera states in two subpopulations are synchronized at weak frequency mismatch, in which the coherent oscillators in them share similar mean phase velocity, and are desynchronized at large frequency mismatch, in which the coherent oscillators in different subpopulations have distinct mean phase velocities. The synchronization–desynchronization transition between chimera states in these two subpopulations is observed with the increase in the frequency mismatch. The observed phenomena are theoretically analyzed by passing to the continuum limit and using the Ott-Antonsen approach.
|
| Keywords
chimera states
bicomponent phase oscillators
nonlocal coupling
desynchronization transition
|
|
Corresponding Author(s):
Fagen Xie,Jun-Zhong Yang
|
|
Issue Date: 21 July 2020
|
|
| 1 |
Y. Kuramoto and D. Battogtokh, Coexistence of coherence and incoherence in nonlocally coupled phase oscillators, Nonlinear Phenom. Complex Syst. 5, 380 (2002)
|
| 2 |
D. M. Abrams and S. H. Strogatz, Chimera states for coupled oscillators, Phys. Rev. Lett. 93(17), 174102 (2004)
https://doi.org/10.1103/PhysRevLett.93.174102
|
| 3 |
C. R. Laing, The dynamics of chimera states in heterogeneous Kuramoto networks, Physica D 238(16), 1569 (2009)
https://doi.org/10.1016/j.physd.2009.04.012
|
| 4 |
A. E. Motter, Nonlinear dynamics: Spontaneous synchrony breaking, Nat. Phys. 6(3), 164 (2010)
https://doi.org/10.1038/nphys1609
|
| 5 |
Y. Zhu, Y. Li, M. Zhang, and J. Yang, The oscillating two-cluster chimera state in non-locally coupled phase oscillators, EPL 97(1), 10009 (2012)
https://doi.org/10.1209/0295-5075/97/10009
|
| 6 |
M. J. Panaggio and D. M. Abrams, Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators, Nonlinearity 28(3), R67 (2015)
https://doi.org/10.1088/0951-7715/28/3/R67
|
| 7 |
E. A. Martens, S. Thutupalli, A. Fourrière, and O. Hallatschek, Chimera states in mechanical oscillator networks, Proc. Natl. Acad. Sci. USA 110(26), 10563 (2013)
https://doi.org/10.1073/pnas.1302880110
|
| 8 |
M. R. Tinsley, S. Nkomo, and K. Showalter, Chimera and phasecluster states in populations of coupled chemical oscillators, Nat. Phys. 8(9), 662 (2012)
https://doi.org/10.1038/nphys2371
|
| 9 |
A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hövel, I. Omelchenko, and E. Schöll, Experimental observation of chimeras in coupled-map lattices, Nat. Phys. 8(9), 658 (2012)
https://doi.org/10.1038/nphys2372
|
| 10 |
H. Cheng, Q. Dai, N. Wu, Y. Feng, H. Li, and J. Yang, Chimera states in nonlocally coupled phase oscillators with biharmonic interaction, Commun. Nonlinear Sci. Numer. Simul. 56, 1 (2018)
https://doi.org/10.1016/j.cnsns.2017.07.015
|
| 11 |
S. S. Gavrilov, Polariton chimeras: Bose–Einstein condensates with intrinsic chaoticity and spontaneous long range ordering, Phys. Rev. Lett. 120(3), 033901 (2018)
https://doi.org/10.1103/PhysRevLett.120.033901
|
| 12 |
H. Xu, G. Wang, L. Huang, and Y. Lai, Chaos in Dirac electron optics: Emergence of a relativistic quantum chimera, Phys. Rev. Lett. 120(12), 124101 (2018)
https://doi.org/10.1103/PhysRevLett.120.124101
|
| 13 |
Z. Wei, F. Parastesh, H. Azarnoush, S. Jafari, D. Ghosh, M. Perc, and M. Slavinec, Nonstationary chimeras in a neuronal network, EPL 123(4), 48003 (2018)
https://doi.org/10.1209/0295-5075/123/48003
|
| 14 |
B. K. Bera, S. Rakshit, D. Ghosh, and J. Kurths, Spike chimera states and firing regularities in neuronal hypernetworks, Chaos 29(5), 053115 (2019)
https://doi.org/10.1063/1.5088833
|
| 15 |
S. Rakshit, B. K. Bera, M. Perc, and D. Ghosh, Basin stability for chimera states, Sci. Rep. 7(1), 2412 (2017)
https://doi.org/10.1038/s41598-017-02409-5
|
| 16 |
B. K. Bera, D. Ghosh, and T. Banerjee, Imperfect traveling chimera states induced by local synaptic gradient coupling, Phys. Rev. E 94(1), 012215 (2016)
https://doi.org/10.1103/PhysRevE.94.012215
|
| 17 |
I. Omelchenko, Y. Maistrenko, P. Hövel, and E. Schöll, Loss of coherence in dynamical networks: Spatial chaos and chimera states, Phys. Rev. Lett. 106(23), 234102 (2011)
https://doi.org/10.1103/PhysRevLett.106.234102
|
| 18 |
I. Omelchenko, A. Zakharova, P. Hövel, J. Siebert, and E. Schöll, Nonlinearity of local dynamics promotes multichimeras, Chaos 25(8), 083104 (2015)
https://doi.org/10.1063/1.4927829
|
| 19 |
I. Omelchenko, O. E. Omelchenko, P. Hövel, and E. Schöll, When nonlocal coupling between oscillators becomes stronger: Patched synchrony or multichimera states, Phys. Rev. Lett. 110(22), 224101 (2013)
https://doi.org/10.1103/PhysRevLett.110.224101
|
| 20 |
J. Hizanidis, V. Kanas, A. Bezerianos, and T. Bountis, Chimera states in networks of nonlocally coupled Hindmarsh–Rose neuron models, Int. J. Bifurcat. Chaos 24(03), 1450030 (2014)
https://doi.org/10.1142/S0218127414500308
|
| 21 |
H. Sakaguchi, Instability of synchronized motion in nonlocally coupled neural oscillators, Phys. Rev. E 73(3), 031907 (2006)
https://doi.org/10.1103/PhysRevE.73.031907
|
| 22 |
J. F. Totz, J. Rode, M. R. Tinsley, K. Showalter, and H. Engel, Spiral wave chimera states in large populations of coupled chemical oscillators, Nat. Phys. 14(3), 282 (2018)
https://doi.org/10.1038/s41567-017-0005-8
|
| 23 |
A. Zakharova, M. Kapeller, and E. Schöll, Chimera death: Symmetry breaking in dynamical networks, Phys. Rev. Lett. 112(15), 154101 (2014)
https://doi.org/10.1103/PhysRevLett.112.154101
|
| 24 |
Y. L. Maistrenko, A. Vasylenko, O. Sudakov, R. Levchenko, and V. L. Maistrenko, Cascades of multiheaded chimera states for coupled phase oscillators, Int. J. Bifurcat. Chaos 24(08), 1440014 (2014)
https://doi.org/10.1142/S0218127414400148
|
| 25 |
E. A. Martens, C. R. Laing, and S. H. Strogatz, Solvable model of spiral wave chimeras, Phys. Rev. Lett. 104(4), 044101 (2010)
https://doi.org/10.1103/PhysRevLett.104.044101
|
| 26 |
C. Gu, G. St-Yves, and J. Davidsen, Spiral wave chimeras in complex oscillatory and chaotic systems, Phys. Rev. Lett. 111(13), 134101 (2013)
https://doi.org/10.1103/PhysRevLett.111.134101
|
| 27 |
S. Guo, Q. Dai, H. Cheng, H. Li, F. Xie, and J. Yang, Spiral wave chimera in two-dimensional nonlocally coupled Fitzhugh–Nagumo systems, Chaos Solitons Fractals 114, 394 (2018)
https://doi.org/10.1016/j.chaos.2018.07.029
|
| 28 |
W. Wang, Q. Dai, H. Cheng, H. Li, and J. Yang, Chimera dynamics in nonlocally coupled moving phase oscillators, Front. Phys. 14(4), 43605 (2019)
https://doi.org/10.1007/s11467-019-0906-3
|
| 29 |
A. Yeldesbay, A. Pikovsky, and M. Rosenblum, Chimeralike states in an ensemble of globally coupled oscillators, Phys. Rev. Lett. 112(14), 144103 (2014)
https://doi.org/10.1103/PhysRevLett.112.144103
|
| 30 |
G. C. Sethia and A. Sen, Chimera states: The existence criteria revisited, Phys. Rev. Lett. 112(14), 144101 (2014)
https://doi.org/10.1103/PhysRevLett.112.144101
|
| 31 |
V. K. Chandrasekar, R. Gopal, A. Venkatesan, and M. Lakshmanan, Mechanism for intensity-induced chimera states in globally coupled oscillators, Phys. Rev. E 90(6), 062913 (2014)
https://doi.org/10.1103/PhysRevE.90.062913
|
| 32 |
K. Premalatha, V. K. Chandrasekar, M. Senthilvelan, and M. Lakshmanan, Impact of symmetry breaking in networks of globally coupled oscillators, Phys. Rev. E 91(5), 052915 (2015)
https://doi.org/10.1103/PhysRevE.91.052915
|
| 33 |
C. R. Laing, Chimeras in networks with purely local coupling, Phys. Rev. E 92, 050904(R) (2015)
https://doi.org/10.1103/PhysRevE.92.050904
|
| 34 |
B. K. Bera, D. Ghosh, and M. Lakshmanan, Chimera states in bursting neurons, Phys. Rev. E 93(1), 012205 (2016)
https://doi.org/10.1103/PhysRevE.93.012205
|
| 35 |
N. Semenova, A. Zakharova, V. Anishchenko, and E. Schöll, Coherence-resonance chimeras in a network of excitable elements, Phys. Rev. Lett. 117(1), 014102 (2016)
https://doi.org/10.1103/PhysRevLett.117.014102
|
| 36 |
Q. Dai, M. Zhang, H. Cheng, H. Li, F. Xie, and J. Yang, From collective oscillation to chimera state in a nonlocally coupled excitable system, Nonlinear Dyn. 91(3), 1723 (2018)
https://doi.org/10.1007/s11071-017-3977-0
|
| 37 |
Y. S. Cho, T. Nishikawa, and A. E. Motter, Stable chimeras and independently synchronizable clusters, Phys. Rev. Lett. 119(8), 084101 (2017)
https://doi.org/10.1103/PhysRevLett.119.084101
|
| 38 |
E. A. Martens, E. Barreto, S. H. Strogatz, E. Ott, P. So, and T. M. Antonsen, Exact results for the Kuramoto model with a bimodal frequency distribution, Phys. Rev. E 79(2), 026204 (2009)
https://doi.org/10.1103/PhysRevE.79.026204
|
| 39 |
S. Ghosh, A. Kumar, A. Zakharova, and S. Jalan, Birth and death of chimera: Interplay of delay and multiplexing, EPL 115(6), 60005 (2016)
https://doi.org/10.1209/0295-5075/115/60005
|
| 40 |
V. A. Maksimenko, V. V. Makarov, B. K. Bera, D. Ghosh, S. K. Dana, M. V. Goremyko, N. S. Frolov, A. A. Koronovskii, and A. E. Hramov, Excitation and suppression of chimera states by multiplexing, Phys. Rev. E 94(5), 052205 (2016)
https://doi.org/10.1103/PhysRevE.94.052205
|
| 41 |
Q. Dai, Q. Liu, H. Cheng, H. Li, and J. Yang, Chimera states in a bipartite network of phase oscillators, Nonlinear Dyn. 92(2), 741 (2018)
https://doi.org/10.1007/s11071-018-4087-3
|
| 42 |
Z. Wu, H. Cheng, Y. Feng, H. Li, Q. Dai, and J. Yang, Chimera states in bipartite networks of FitzHugh–Nagumo oscillators, Front. Phys. 13(2), 130503 (2018)
https://doi.org/10.1007/s11467-017-0737-z
|
| 43 |
Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer Series in Synergetics, Berlin: Springer-Verlag, 1984
https://doi.org/10.1007/978-3-642-69689-3
|
| 44 |
J. A. Acebrón, L. L. Bonilla, C. J. Pérez Vicente, F. Ritort, and R. Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena, Rev. Mod. Phys. 77(1), 137 (2005)
https://doi.org/10.1103/RevModPhys.77.137
|
| 45 |
E. Ott and T. M. Antonsen, Low dimensional behavior of large systems of globally coupled oscillators, Chaos 18(3), 037113 (2008)
https://doi.org/10.1063/1.2930766
|
| 46 |
O. E. Omel’chenko, Coherence-incoherence patterns in a ring of non-locally coupled phase oscillators, Nonlinearity 26(9), 2469 (2013)
https://doi.org/10.1088/0951-7715/26/9/2469
|
| 47 |
M. Wolfrum and O. E. Omel’chenko, Chimera states are chaotic transients, Phys. Rev. E 84(1), 015201 (2011)
https://doi.org/10.1103/PhysRevE.84.015201
|
| 48 |
B. Pietras, N. Deschle, and A. Daffertshofer, Equivalence of coupled networks and networks with multimodal frequency distributions: Conditions for the bimodal and trimodal case, Phys. Rev. E 94, 052211 (2011)
https://doi.org/10.1103/PhysRevE.94.052211
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
| |
Shared |
|
|
|
|
| |
Discussed |
|
|
|
|
