Skip to main content
SpringerLink
Log in

Network synchronization under periodic coupling of both positive and negative values

  • Regular Article - Statistical and Nonlinear Physics
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We revisit a system of networked chaotic oscillators subjected to a common periodic coupling, where the coupling is governed by constant coupling strength, coupling frequency, and coupling amplitude. Utilizing the method of master stability function, the effect of periodic coupling on network synchronization is analyzed in detail, and numerical results are verified. It is found that when the coupling is a mixture of both periodic positive and negative couplings, the performance of network synchronization is better than that of periodic positive coupling. Utilizing the approach of finite-time Lyapunov exponent, we find the mechanism for the maximized synchronization performance, that is, the power spectrum of the finite-time Lyapunov exponent, at the characteristic frequencies, is varied from local to wide distributions. If this feature is missing or less prominent, the periodic coupling has less effect on synchronization performance. Our study indicates the validity of the finite-time Lyapunov exponent approach in detecting the synchronization behavior of coupled oscillators and is helpful for grasping the collective behavior of networks with positive and negative couplings.

Graphical abstract

1. Periodic coupling enables synchronization in an infinite range of the constant coupling strength by tuning the coupling frequency or the coupling amplitude (left panel). 2. The high frequency of periodic coupling can also achieve enhanced synchronization (right panel). 3. We use the FTLE approach to reveal the underlying mechanism of synchronization. It is found that the optimized synchronization is attributed to the drastic response of the FTLE approach to periodic coupling.

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

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The results are obtained mainly through numerical simulation, and all the related data have been shown in the figures of the article.]

References

  1. F. Battiston, G. Cencetti, I. Iacopini, V. Latora, M. Lucas, A. Patania, J.G. Young, G. Petri, Phys. Rep. 874, 1 (2020)

    ADS  MathSciNet  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  3. S. Boccaletti, J.A. Almendral, S. Guan, I. Leyva, Z. Liu, I. Sendiña-Nadal, Z. Wang, Y. Zou, Phys. Rep. 660, 1 (2016)

    ADS  MathSciNet  Google Scholar 

  4. A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, C.S. Zhou, Phys. Rep. 469, 93 (2008)

    ADS  MathSciNet  Google Scholar 

  5. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear Science (Cambridge University Press, Cambridge, 2003)

    MATH  Google Scholar 

  6. S. Boccaletti, J. Kurths, G. Osipov, D.L. Valladares, C.S. Zhou, Phys. Rep. 366, 1 (2002)

    ADS  MathSciNet  Google Scholar 

  7. M.S. Anwar, D. Ghosh, Phys. Rev. E 106, 034314 (2022)

    ADS  Google Scholar 

  8. D. Ghosh, M. Frasca, A. Rizzo, S. Majhi, S. Rakshit, K. Alfaro-Bittner, S. Boccaletti, Phys. Rep. 949, 1 (2022)

    ADS  MathSciNet  Google Scholar 

  9. A. Bayani, S. Jafari, H. Azarnoush, F. Nazarimehr, S. Boccaletti, M. Perc, Chaos Solit. Fract. 169, 113243 (2023)

    Google Scholar 

  10. S. Majhi, M. Perc, D. Ghosh, J. R. Soc. Interface 19, 20220043 (2022)

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

    ADS  Google Scholar 

  12. G. Hu, J.Z. Yang, W.J. Liu, Phys. Rev. E 58, 4440 (1998)

    ADS  Google Scholar 

  13. L. Huang, Q.F. Chen, Y.C. Lai, L.M. Pecora, Phys. Rev. E 80, 036204 (2009)

    ADS  Google Scholar 

  14. P. Holme, J. Saramäki, Phys. Rep. 519, 97 (2012)

    ADS  Google Scholar 

  15. A. Li, S.P. Cornelius, Y.Y. Liu, L. Wang, A.L. Barabási, Science 358, 1042 (2017)

    ADS  Google Scholar 

  16. S.N. Dorogovtsev, J.F.F. Mendes, Adv. Phys. 51, 1079 (2002)

    ADS  Google Scholar 

  17. G. Szabó, G. Fáth, Phys. Rep. 446, 97 (2007)

    ADS  MathSciNet  Google Scholar 

  18. I.V. Belykh, V.N. Belykh, M. Hasler, Physica D 195, 188 (2004)

    ADS  MathSciNet  Google Scholar 

  19. M. Porfiri, Phys. Rev. E 85, 056114 (2012)

    ADS  Google Scholar 

  20. M. Hasler, V.N. Belykh, I.V. Belykh, SIAM J. Appl. Dyn. Syst. 12, 1007 (2013)

    MathSciNet  Google Scholar 

  21. M. Frasca, A. Buscarino, A. Rizzo, L. Fortuna, S. Boccaletti, Phys. Rev. Lett. 100, 044102 (2008)

    ADS  Google Scholar 

  22. V. Kohar, P. Ji, A. Choudhary, S. Sinha, J. Kurths, Phys. Rev. E 90, 022812 (2014)

    ADS  Google Scholar 

  23. N. Fujiwara, J. Kurths, A. Diáz-Guilera, Chaos 26, 094824 (2016)

    ADS  MathSciNet  Google Scholar 

  24. F. Parastesh, K. Rajagopal, S. Jafari, M. Perc, E. Schöll, Phys. Rev. E 105, 054304 (2022)

    ADS  Google Scholar 

  25. T. Moalemi, F. Parastesh, T. Kapitaniak, Eur. Phys. J. Spec. Top. 231, 3961 (2022)

    Google Scholar 

  26. F. Sorrentino, E. Ott, Phys. Rev. Lett. 100, 114101 (2008)

    ADS  Google Scholar 

  27. J. Zhou, Y. Zou, S.G. Guan, Z.H. Liu, S. Boccaletti, Sci. Rep. 6, 35979 (2016)

    ADS  Google Scholar 

  28. A.E. Motter, Y.C. Lai, Phys. Rev. E 66, 065102 (2002)

    ADS  Google Scholar 

  29. P. Holme, M.E.J. Newman, Phys. Rev. E 74, 056108 (2006)

    ADS  Google Scholar 

  30. I.B. Schwartz, L.B. Shaw, Physics 3, 17 (2010)

    Google Scholar 

  31. Y.F. Wang, H.W. Fan, W.J. Lin, Y.C. Lai, X.G. Wang, Sci. Rep. 6, 24445 (2016)

    ADS  Google Scholar 

  32. L. Chen, C. Qiu, H.B. Huang, Phys. Rev. E 79, 045101 (2009)

    ADS  Google Scholar 

  33. M. Schröder, M. Mannattil, D. Dutta, S. Chakraborty, M. Timme, Phys. Rev. Lett. 115, 054101 (2015)

    ADS  Google Scholar 

  34. A. Buscarino, M. Frasca, M. Branciforte, L. Fortuna, J.C. Sprott, Nonlinear Dyn. 88, 673 (2017)

    Google Scholar 

  35. S.S. Li, N. Sun, L. Chen, X.G. Wang, Phys. Rev. E 98, 012304 (2018)

    ADS  Google Scholar 

  36. Z. Dayani, F. Parastesh, F. Nazarimehr, K. Rajagopal, S. Jafari, E. Schöll, J. Kurths, Chaos 33, 033139 (2023)

    ADS  Google Scholar 

  37. S. Mirzaei, M.S. Anwar, F. Parastesh, S. Jafari, D. Ghosh, Phys. Rev. E 107, 014201 (2023)

    ADS  Google Scholar 

  38. X.M. Liang, C. Liu, X.Y. Zhang, Phys. Rev. E 101, 022205 (2020)

    ADS  MathSciNet  Google Scholar 

  39. L.X. Yang, J. Jiang, X.J. Liu, Physica A 514, 916 (2019)

  40. O.E. Rössler, Phys. Lett. A 57, 397 (1976)

    ADS  Google Scholar 

  41. A. Pikovsky, Chaos 3, 225 (1993)

  42. A. Prasad, R. Ramaswamy, Phys. Rev. E 60, 2761 (1999)

    ADS  Google Scholar 

  43. X.G. Wang, Y.C. Lai, C.H. Lai, Phys. Rev. E 74, 016203 (2006)

    ADS  Google Scholar 

  44. K. Stefański, K. Buszko, K. Piecyk, Chaos 20, 033117 (2010)

    ADS  MathSciNet  Google Scholar 

  45. A.E. Botha, Sci. Rep. 6, 29213 (2016)

    ADS  Google Scholar 

  46. E.N. Lorenz, J. Atmos. Sci. 20, 130 (1963)

    ADS  Google Scholar 

Download references

Acknowledgements

The Author would like to gratefully acknowledge X. G. Wang, Y. F. Wang, and H. W. Fan, for the many discussions. The Author would also like to gratefully acknowledge and thank the anonymous reviewers and the editors for their constructive comments. This work was supported by the National Natural Science Foundation of China under the Grant No. 12102004, the Natural Science Foundation of Ningxia under the Grant No. 2020AAC03240, the Research Foundation of North Minzu University under the Grant No. 2020XYZSX06 and 2020KYQD05.

Author information

Authors and Affiliations

  1. School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, China

    Sansan Li

Authors
  1. Sansan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sansan Li.

Ethics declarations

Conflict of interest

The author declares that he has no conflicts of interest or personal relationships that could have appeared to impact the work reported in this paper.

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

Li, S. Network synchronization under periodic coupling of both positive and negative values. Eur. Phys. J. B 96, 88 (2023). https://doi.org/10.1140/epjb/s10051-023-00559-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-023-00559-2

Search

Navigation