Skip to main content
SpringerLink
Log in

Various amplitude chimeras in locally coupled limit-cycle oscillators: impact of coupled system size

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

We investigate chimera states in two networks of locally coupled identical paradigmatic limit-cycle oscillators, which are the van der Pol oscillator and the Rayleigh oscillator. The interplay between local dynamics, local coupling, size of the system, and specially prepared initial conditions allows the two ring-networks to generate a lot of amplitude chimera states; a basic amplitude chimera state being a self-organized state made up of spatially separated domains of synchronous oscillations with a large amplitude and asynchronous oscillations with disparate smaller amplitudes and drifting centers of mass. Apart from this classical amplitude chimera state, we report the occurrence of damped amplitude chimera and stable amplitude chimera states that were found previously, and two novel stable amplitude chimera states, namely, traveling amplitude chimera and snaking amplitude chimera states. The traveling amplitude chimera state, that emerges in coupled systems with relatively large size, involves a strongly localized incoherent region that moves slowly and uniformly along the ring-network. As for the snaking amplitude chimera state, that seldom occurs, its incoherent region(s) snakes (snake, respectively) regularly around a fixed position (fixed positions, respectively). Furthermore, while examining the features of the chimera states with respect to the size of the coupled systems, we find that the lifetime of transient amplitude chimera patterns increases with the size of the coupled system. A result that is contrary to previous findings.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Data Availability

No datasets were generated or analyzed during the current study.

References

  1. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear Science (Cambridge University Press, Cambridge, UK, 2001)

    Book  Google Scholar 

  2. S. Strogatz, Sync: The Emerging Science of Spontaneous Order (Hyperion, New York, 2003)

    Google Scholar 

  3. A. Balanov, N. Janson, D. Postnov, O. Sosnovtseva, Synchronization: From Simple to Complex (Springer-Verlag, Berlin Heidelberg, 2009)

    Google Scholar 

  4. Y. Kuramoto, D. Battogtokh, Nonlinear Phenom. Complex Syst. 5, 380 (2002)

    Google Scholar 

  5. D.M. Abrams, S.H. Strogatz, Phys. Rev. Lett. 93, 174102 (2004)

    Article  ADS  PubMed  Google Scholar 

  6. M.J. Panaggio, D.M. Abrams, Nonlinearity 28, R67 (2015)

    Article  ADS  Google Scholar 

  7. E. Schöll, Eur. Phys. J. Spec. Top. 225, 891 (2016)

    Article  Google Scholar 

  8. F.P. Kemeth, S.W. Haugland, L. Schmidt, I.G. Kevrekidis, K. Krischer, Chaos 26, 094815 (2016)

    Article  ADS  PubMed  Google Scholar 

  9. O.E. Omel’chenko, Nonlinearity 31, R121 (2018)

    Article  ADS  Google Scholar 

  10. A. Zakharova, Chimera Patterns in Networks: Interplay between Dynamics, Structure, Noise, and Delay (Springer Nature Switzerland AG, Cham, 2020)

    Book  Google Scholar 

  11. F. Parastesh, S. Jafari, H. Azarnoush, Z. Shahriari, Z. Wang, S. Boccaletti, M. Perc, Phys. Rep. 898, 1 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  12. S.W. Haugland, J. Phys. Complex. 2, 032001 (2021)

    Article  ADS  Google Scholar 

  13. A. Koseska, E. Volkov, J. Kurths, Phys. Rep. 531, 173 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  14. W. Zou, D.V. Senthilkumar, M. Zhan, J. Kurths, Phys. Rep. 931, 1 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  15. A. Zakharova, M. Kapeller, E. Schöll, Phys. Rev. Lett. 112, 154101 (2014)

    Article  ADS  PubMed  Google Scholar 

  16. M. Wolfrum, O.E. Omel’chenko, Phys. Rev. E 84, 015201 (2011)

    Article  ADS  Google Scholar 

  17. D.P. Rosin, D. Rontani, N.D. Haynes, E. Schöll, D.J. Gauthier, Phys. Rev. E 90, 030902(R) (2014)

    Article  ADS  Google Scholar 

  18. S.A.M. Loos, J.C. Claussen, E. Schöll, Phys. Rev. E 93, 012209 (2016)

    Article  ADS  PubMed  Google Scholar 

  19. L. Tumash, A. Zakharova, J. Lehnert, W. Just, E. Schöll, Europhys. Lett. 117, 20001 (2017)

    Article  ADS  Google Scholar 

  20. K. Premalatha, V.K. Chandrasekar, M. Senthilvelan, M. Lakshmanan, Chaos 28, 033110 (2018)

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  21. K. Sathiyadevi, V.K. Chandrasekar, D.V. Senthilkumar, Phys. Rev. E 98, 032301 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  22. B. Bandyopadhyay, T. Khatun, P.S. Dutta, T. Banerjee, Chaos Soliton. Fract. 139, 110289 (2020)

    Article  Google Scholar 

  23. S. G. Ngueuteu Mbouna, T. Banerjee, E. Schöll, R. Yamapi, Chaos 33, 063137 (2023)

  24. S. G. Ngueuteu Mbouna, T. Banerjee, R. Yamapi, P. Woafo, Chaos Soliton. Fract. 157, 111945 (2022)

  25. D. Kaplan, L. Glass, Understanding Nonlinear Dynamics (Springer-Verlag, New York, 1995)

    Book  Google Scholar 

  26. T. Kanamaru, Scholarpedia 2, 2202 (2007)

    Article  ADS  Google Scholar 

  27. I. Omelchenko, A. Zakharova, P. Hövel, J. Siebert, E. Schöll, Chaos 25, 083104 (2015)

    Article  ADS  MathSciNet  PubMed  Google Scholar 

  28. V.M. Bastidas, I. Omelchenko, A. Zakharova, E. Schöll, Phys. Rev. E 92, 062924 (2015)

    Article  ADS  CAS  Google Scholar 

  29. C.R. Hens, A. Mishra, P.K. Roy, A. Sen, S.K. Dana, Pramana 84, 229 (2015)

    Article  ADS  Google Scholar 

  30. S. Ulonska, I. Omelchenko, A. Zakharova, E. Schöll, Chaos 26, 094825 (2016)

    Article  ADS  MathSciNet  PubMed  Google Scholar 

  31. E. Njinkeu Nganso, S. G. Ngueuteu Mbouna, R. Yamapi, G. Filatrella, J. Kurths, Chaos Soliton. Fract. 169, 113235 (2023)

  32. A. Koseska, E. Volkov, J. Kurths, Phys. Rev. Lett. 111, 024103 (2013)

    Article  ADS  PubMed  Google Scholar 

  33. D. Ghosh, T. Banerjee, J. Kurths, Phys. Rev. E 92, 052908 (2015)

    Article  ADS  Google Scholar 

  34. D.V. Senthilkumar, K. Suresh, V.K. Chandrasekar, W. Zou, S.K. Dana, T. Kathamuthu, J. Kurths, Chaos 26, 043112 (2016)

    Article  ADS  CAS  PubMed  Google Scholar 

  35. U.K. Verma, A. Sharma, N.K. Kamal, M.D. Shrimali, Chaos 29, 063127 (2019)

    Article  ADS  MathSciNet  PubMed  Google Scholar 

  36. N. Zhao, Z. Sun, X. Yang, W. Xu, Phys. Rev. E 97, 062203 (2018)

    Article  ADS  CAS  PubMed  Google Scholar 

  37. T. Banerjee, D. Biswas, D. Ghosh, E. Schöll, A. Zakharova, Chaos 28, 113124 (2018)

    Article  ADS  MathSciNet  PubMed  Google Scholar 

  38. I. Schneider, M. Kapeller, S. Loos, A. Zakharova, B. Fiedler, E. Schöll, Phys. Rev. E 92, 052915 (2015)

    Article  ADS  Google Scholar 

  39. T. Banerjee, Europhys. Lett. 110, 60003 (2015)

    Article  ADS  Google Scholar 

  40. L.M. Pecora, T.L. Carroll, Phys. Rev. Lett. 80, 2109 (1998)

    Article  ADS  CAS  Google Scholar 

  41. J.F. Heagy, T.L. Carroll, L.M. Pecora, Phys. Rev. E 50, 1874 (1994)

    Article  ADS  CAS  Google Scholar 

  42. R. Gopal, V.K. Chandrasekar, A. Venkatesan, M. Lakshmanan, Phys. Rev. E 89, 052914 (2014)

    Article  ADS  CAS  Google Scholar 

  43. G.C. Sethia, A. Sen, G.L. Johnston, Phys. Rev. E 88, 042917 (2013)

    Article  ADS  Google Scholar 

  44. J. Sawicki, I. Omelchenko, A. Zakharova, E. Schöll, Phys. Rev. E 98, 062224 (2018)

    Article  ADS  CAS  Google Scholar 

  45. B.K. Bera, D. Ghosh, T. Banerjee, Phys. Rev. E 94, 012215 (2016)

    Article  ADS  PubMed  Google Scholar 

  46. J. Xie, E. Knobloch, H.-C. Kao, Phys. Rev. E 90, 022919 (2014)

    Article  ADS  Google Scholar 

  47. A. Mishra, S. Saha, D. Ghosh, G.V. Osipov, S.K. Dana, Opera Med. Physiol. 3, 14 (2017)

    Google Scholar 

  48. A.J. Alvarez-Socorro, M.G. Clerc, N. Verschueren, Commun. Nonlinear Sci. Numer. Simulat. 94, 105559 (2021)

    Article  Google Scholar 

  49. O.E. Omel’chenko, J. Phys. A: Math. Theor. 52, 104001 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  50. G.B. Soh, P. Louodop, R. Kengne, R. Tchitnga, Heliyon 6, e03739 (2020)

    Article  Google Scholar 

Download references

Acknowledgements

This work is partially funded by the Center for Nonlinear Systems, Chennai Institute of Technology, India via funding number CIT/CNS/2023/Rp-007.

Author information

Authors and Affiliations

  1. Center for Computational Modelling, Chennai Institut of Technology, Chennai, Tamilnadu, 600069, India

    Prasina Alexander

  2. Department of Architecture and Engineering Arts, Fine Arts Institute, University of Dschang, P. O. Box 31, Foumban, Cameroon

    A. N. Ndoukouo

  3. Laboratory of Modeling and Simulation in Engineering, Biomimetics and Prototypes, Faculty of Science, University of Yaoundé I, P. O. Box 812, Yaoundé, Cameroon

    S. G. Ngueuteu Mbouna

  4. Center for Nonlinear Systems, Chennai Institut of Technology, Chennai, Tamilnadu, 600069, India

    Karthikeyan Rajagopal

Authors
  1. Prasina Alexander
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. N. Ndoukouo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. G. Ngueuteu Mbouna
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Karthikeyan Rajagopal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. G. Ngueuteu Mbouna.

Ethics declarations

Conflict of interest

The authors declare that they have no conflicts to disclose.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alexander, P., Ndoukouo, A.N., Mbouna, S.G.N. et al. Various amplitude chimeras in locally coupled limit-cycle oscillators: impact of coupled system size. Eur. Phys. J. Plus 139, 186 (2024). https://doi.org/10.1140/epjp/s13360-024-04978-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-024-04978-7

Search

Navigation