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Nonlinear Dynamics

, Volume 92, Issue 2, pp 741–749 | Cite as

Chimera states in a bipartite network of phase oscillators

  • Qionglin Dai
  • Qian Liu
  • Hongyan Cheng
  • Haihong Li
  • Junzhong Yang
Original Paper

Abstract

The chimera state, exhibiting a hybrid state of coexisting coherent and incoherent behaviors, has become a fast growing field in the past decade. In this paper, we investigate bipartite networks of nonlocally coupled phase oscillators. We report different types of chimera states such as in-phase chimera states, anti-phase chimera states, and syn-desyn chimera states. Phase diagrams on different parameter planes are presented.

Keywords

Chimera states Bipartite networks Nonlocal coupling Phase oscillators 

Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Nos. 11575036 and 11505016).

References

  1. 1.
    Kuramoto, Y., Battogtokh, D.: Coexistence of coherence and incoherence in nonlocally coupled phase oscillators. Nonlinear Phenom. Complex Syst. 5, 380–385 (2002)Google Scholar
  2. 2.
    Abrams, D.M., Strogatz, S.H.: Chimera states for coupled oscillators. Phys. Rev. Lett. 93, 174102 (2004)CrossRefGoogle Scholar
  3. 3.
    Motter, A.E.: Nonlinear dynamics: spontaneous synchrony breaking. Nat. Phys. 6, 164–165 (2010)CrossRefGoogle Scholar
  4. 4.
    Martens, E.A., Thutupalli, S., Fourrière, A., Hallatschek, O.: Chimera states in mechanical oscillator networks. Proc. Nat. Acad. Sci. USA 110, 10563–10567 (2013)CrossRefGoogle Scholar
  5. 5.
    Zhu, Y., Li, Y., Zhang, M., Yang, J.: The oscillating two-cluster chimera state in non-locally coupled phase oscillators. EPL 97, 10009 (2012)CrossRefGoogle Scholar
  6. 6.
    Panaggio, M.J., Abrams, D.M.: Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators. Nonlinearity 28, R67 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Tinsley, M.R., Nkomo, S., Showalter, K.: Chimera and phase-cluster states in populations of coupled chemical oscillators. Nat. Phys. 8, 662–665 (2012)CrossRefGoogle Scholar
  8. 8.
    Hagerstrom, A.M., Murphy, T.E., Roy, R., Hövel, P., Omelchenko, I., Schöll, E.: Experimental observation of chimeras in coupled-map lattices. Nat. Phys. 8, 658–661 (2012)CrossRefGoogle Scholar
  9. 9.
    Olmi, S., Martens, E.A., Thutupalli, S., Torcini, A.: Intermittent chaotic chimeras for coupled rotators. Phys. Rev. E 92, 030901(R) (2015)CrossRefGoogle Scholar
  10. 10.
    Zakharova, A., Kapeller, M., Schöll, E.: Chimera death: symmetry breaking in dynamical networks. Phys. Rev. Lett. 112, 154101 (2014)CrossRefGoogle Scholar
  11. 11.
    Omelchenko, I., Provata, A., Hizanidis, J., Schöll, E., Hövel, P.: Robustness of chimera states for coupled FitzHugh-Nagumo oscillators. Phys. Rev. E 91, 022917 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Maistrenko, Y.L., Vasylenko, A., Sudakov, O., Levchenko, R., Maistrenko, V.L.: Cascades of multiheaded chimera states for coupled phase oscillators. Int. J. Bifurcat. Chaos 24, 1440014 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Omelchenko, I., Maistrenko, Y., Hövel, P., Schöll, E.: Loss of coherence in dynamical networks: spatial chaos and chimera states. Phys. Rev. Lett. 106, 234102 (2011)CrossRefGoogle Scholar
  14. 14.
    Laing, C.R.: Chimeras in networks of planar oscillators. Phys. Rev. E 81, 066221 (2010)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Omelchenko, I., Zakharova, A., Hövel, P., Siebert, J., Schöll, E.: Nonlinearity of local dynamics promotes multi-chimeras. Chaos 25, 083104 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Omelchenko, I., Omelchenko, O.E., Hövel, P., Schöll, E.: When nonlocal coupling between oscillators becomes stronger: patched synchrony or multichimera states. Phys. Rev. Lett. 110, 224101 (2013)CrossRefGoogle Scholar
  17. 17.
    Hizanidis, J., Kanas, V., Bezerianos, A., Bountis, T.: Chimera states in networks of nonlocally coupled Hindmarsh-Rose neuron models. Int. J. Bifurcat. Chaos 24, 1450030 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Sakaguchi, H.: Instability of synchronized motion in nonlocally coupled neural oscillators. Phys. Rev. E 73, 031907 (2006)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Larger, L., Penkovsky, B., Maistrenko, Y.: Virtual chimera states for delayed-feedback systems. Phys. Rev. Lett. 111, 054103 (2013)CrossRefGoogle Scholar
  20. 20.
    Yeldesbay, A., Pikovsky, A., Rosenblum, M.: Chimeralike states in an ensemble of globally coupled oscillators. Phys. Rev. Lett. 112, 144103 (2014)CrossRefGoogle Scholar
  21. 21.
    Sethia, G.C., Sen, A.: Chimera states: the existence criteria revisited. Phys. Rev. Lett. 112, 144101 (2014).  https://doi.org/10.1103/PhysRevLett.112.144101 CrossRefGoogle Scholar
  22. 22.
    Chandrasekar, V.K., Gopal, R., Venkatesan, A., Lakshmanan, M.: Mechanism for intensity-induced chimera states in globally coupled oscillators. Phys. Rev. E 90, 062913 (2014)CrossRefGoogle Scholar
  23. 23.
    Premalatha, K., Chandrasekar, V.K., Senthilvelan, M., Lakshmanan, M.: Impact of symmetry breaking in networks of globally coupled oscillators. Phys. Rev. E 91, 052915 (2015)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Laing, C.R.: Chimeras in networks with purely local coupling. Phys. Rev. E 92, 050904(R) (2015)CrossRefGoogle Scholar
  25. 25.
    Bera, B.K., Ghosh, D., Lakshmanan, M.: Chimera states in bursting neurons. Phys. Rev. E 93, 012205 (2016)Google Scholar
  26. 26.
    Bera, B.K., Ghosh, D., Banerjee, T.: Imperfect traveling chimera states induced by local synaptic gradient coupling. Phys. Rev. E 94, 012215 (2016)CrossRefGoogle Scholar
  27. 27.
    Martens, E.A., Laing, C.R., Strogatz, S.H.: Solvable model of spiral wave chimeras. Phys. Rev. Lett. 104, 044101 (2010)CrossRefGoogle Scholar
  28. 28.
    Gu, C., St-Yves, G., Davidsen, J.: Spiral wave chimeras in complex oscillatory and chaotic systems. Phys. Rev. Lett. 111, 134101 (2013)CrossRefGoogle Scholar
  29. 29.
    Panaggio, M.J., Abrams, D.M.: Chimera states on a flat torus. Phys. Rev. Lett. 110, 094102 (2013)CrossRefGoogle Scholar
  30. 30.
    Panaggio, M.J., Abrams, D.M.: Chimera states on the surface of a sphere. Phys. Rev. E 91, 022909 (2015)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Zhu, Y., Zheng, Z., Yang, J.: Chimera states on complex networks. Phys. Rev. E 89, 022914 (2014)CrossRefGoogle Scholar
  32. 32.
    Yao, N., Huang, Z., Lai, Y., Zheng, Z.: Robustness of chimera states in complex dynamical systems. Sci. Rep. 3, 3522 (2013)CrossRefGoogle Scholar
  33. 33.
    Ghosh, S., Kumar, A., Zakharova, A., Jalan, S.: Birth and death of chimera: interplay of delay and multiplexing. EPL 115, 60005 (2016)CrossRefGoogle Scholar
  34. 34.
    Maksimenko, V.A., Makarov, V.V., Bera, B.K., Ghosh, D., Dana, S.K., Goremyko, M.V., Frolov, N.S., Koronovskii, A.A., Hramov, A.E.: Excitation and suppression of chimera states by multiplexing. Phys. Rev. E 94, 052205 (2016)CrossRefGoogle Scholar
  35. 35.
    Majhi, S., Perc, M., Ghosh, D.: Chimera states in uncoupled neurons induced by a multilayer structure. Sci. Rep. 6, 39033 (2016)CrossRefGoogle Scholar
  36. 36.
    Tsimring, L.S., Rulkov, N.F., Larsen, M.L., Gabbay, M.: Repulsive synchronization in an array of phase oscillators. Phys. Rev. Lett. 95, 014101 (2005)CrossRefGoogle Scholar
  37. 37.
    Hong, H., Strogatz, S.H.: Kuramoto model of coupled oscillators with positive and negative coupling parameters: an example of conformist and contrarian oscillators. Phys. Rev. Lett. 106, 054102 (2011)CrossRefGoogle Scholar
  38. 38.
    Ju, P., Yang, J.: Synchronization dynamics in a system of multiple interacting populations of phase oscillators. Chin. Phys. Lett. 32, 030502 (2015)CrossRefGoogle Scholar
  39. 39.
    Wolfrum, M., Omelchenko, O.E.: Chimera states are chaotic transients. Phys. Rev. E 84, 015201 (2011)CrossRefGoogle Scholar
  40. 40.
    Ott, E., Antonsen, T.M.: Low dimensional behavior of large systems of globally coupled oscillators. Chaos 18, 037113 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Laing, C.R.: The dynamics of chimera states in heterogeneous Kuramoto networks. Physica D 238, 1569–1588 (2009)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of ScienceBeijing University of Posts and TelecommunicationsBeijingChina

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