Skip to main content
SpringerLink
Log in

Mobile Dissipative Breathers in a Chain of Nonlinear Oscillators

  • Published:
Technical Physics Letters Aims and scope Submit manuscript

Abstract

In a numerical experiment, it is found that at least three localized stationary breather type modes can exist in a chain of Rayleigh oscillators with a nonlinear coupling between them: immobile, “slow,” and “fast” dissipative breathers. The dynamics of synchronous motions of chain elements depends on the relation of characteristic time scales of the system related to the frequency of the oscillators and rigidity of the coupling between them; it is multistable.

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.

Similar content being viewed by others

REFERENCES

  1. A. J. Sievers and S. Takeno, Phys. Rev. Lett. 61, 970 (1988).

    Article  ADS  Google Scholar 

  2. S. V. Dmitriev, E. A. Korznikova, J. A. Baimova, and M. G. Velarde, Phys. Usp. 59, 446 (2016).

    Article  ADS  Google Scholar 

  3. P. Romanczuk, M. Bär, W. Ebeling, B. Lindner, and L. Schimansky-Geier, Eur. Phys. J. Spec. Top. 202, 1 (2012).

    Article  Google Scholar 

  4. E. del Río, V. A. Makarov, M. G. Velarde, and W. Ebeling, Phys. Rev. E 67, 056208 (2003).

    Article  ADS  Google Scholar 

  5. S. J. Thomson, M. M. P. Couchman, and J. W. M. Bush, arXiv:2001.09165v1 [pcond-mat.soft] (2020).

  6. T. Endo and S. Mori, IEEE Trans. Circuits Syst. 25, 7 (1978).

    Article  Google Scholar 

  7. M. Rosenblum and A. Pikovsky, Phys. Rev. Lett. 92, 114102 (2004).

    Article  ADS  Google Scholar 

  8. A. V. Shabunin, A. A. Akopov, V. V. Astakhov, and T. E. Vadivasova, Izv. Vyssh. Uchebn. Zaved., Prikl. Nelin. Din. 13 (4), 37 (2005).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  10. A. P. Chetverikov, K. S. Sergeev, and E. del Rio, Int. J. Bifurc. Chaos 28, 1830027 (2018).

    Article  Google Scholar 

  11. A. P. Chetverikov, K. S. Sergeev, and E. del Rio, Phys. A (Amsterdam, Neth.) 513, 147 (2018).

  12. K. S. Sergeev and A. P. Chetverikov, Nelin. Din. 12, 341 (2016).

    Article  Google Scholar 

Download references

Funding

A.P. Chetverikov (development of the mathematical model and description of the attraction basin structure) acknowledges the support of the Russian Foundation for Basic Research within the framework of joint scientific project with the German Research Foundation no. 20-52-12004. K.S. Sergeev (carrying out the numerical experiment and work on the text of the paper) acknowledges the support of the Russian Science Foundation, project no. 20-12-00119.

Author information

Authors and Affiliations

  1. Saratov State University, 410012, Saratov, Russia

    K. S. Sergeev, E. M. Elizarov & A. P. Chetverikov

Authors
  1. K. S. Sergeev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. M. Elizarov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. P. Chetverikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. S. Sergeev.

Ethics declarations

The authors declare that they have no conflict of interest.

Additional information

Translated by A. Nikol’skii

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sergeev, K.S., Elizarov, E.M. & Chetverikov, A.P. Mobile Dissipative Breathers in a Chain of Nonlinear Oscillators. Tech. Phys. Lett. 46, 1068–1071 (2020). https://doi.org/10.1134/S1063785020110127

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063785020110127

Keywords:

Search

Navigation