Skip to main content
SpringerLink
Log in

Traveling patterns in a network of memristor-based oscillators with extreme multistability

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

Abstract

The study of collective behaviors in the networks of memristive systems has achieved negligible attention. In this paper, a ring network of memristive based Wien-bridge oscillators is investigated. The Wien-bridge oscillator exhibits extreme multistability. Therefore, the initial conditions of the network can play an important role in the emergence of different spatiotemporal patterns. Here, the initial conditions are chosen in a small region, in which a single oscillator shows various attractors with similar topologies. It is observed that by varying the coupling strength and coupling range, various patterns are formed. In most of the appeared patterns, the traveling of coexistent coherent and incoherent oscillators is observed, whether in a part of the pattern or in the whole. It seems that the traveling patterns are formed due to the multistability of the oscillators and their time-scaled time series. Overall, by varying the coupling parameters, several patterns such as chimera state, traveling chimera and nonstationary chimera, are emerged in the network.

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

Similar content being viewed by others

References

  1. L. Chua, IEEE Trans. Circuit Theory 18, 507 (1971)

    Article  Google Scholar 

  2. S. Yang, Z. Guo, J. Wang, IEEE Trans. Syst. Man Cybern. Syst. 45, 1077 (2015)

    Article  Google Scholar 

  3. T. Driscoll, H.-T. Kim, B.-G. Chae, M. Di Ventra, D. Basov, Appl. Phys. Lett. 95, 043503 (2009)

    Article  ADS  Google Scholar 

  4. M. Lv, C. Wang, G. Ren, J. Ma, X. Song, Nonlinear Dyn. 85, 1479 (2016)

    Article  Google Scholar 

  5. Y. Xu, H. Ying, Y. Jia, J. Ma, T. Hayat, Sci. Rep. 7, 43452 (2017)

    Article  ADS  Google Scholar 

  6. J. Ma, P. Zhou, B. Ahmad, G. Ren, C. Wang, PloS One 13, e0191120 (2018)

    Article  Google Scholar 

  7. V.T. Pham, S. Jafari, S. Vaidyanathan, C. Volos, X. Wang, Sci. China Technol. Sci. 59, 358 (2016)

    Article  Google Scholar 

  8. K. Rajagopal, A. Bayani, A.J.M. Khalaf, H. Namazi, S. Jafari, V.-T. Pham, AEU-Int. J. Electron. Commun. 95, 207 (2018)

    Article  Google Scholar 

  9. N. Wang, B. Bao, T. Jiang, M. Chen, Q. Xu, Math. Prob. Eng. 2017, 13 (2017)

    Google Scholar 

  10. G. Zhang, J. Ma, A. Alsaedi, B. Ahmad, F. Alzahrani, Appl. Math. Comput. 321, 290 (2018)

    MathSciNet  Google Scholar 

  11. B. Bao, T. Jiang, G. Wang, P. Jin, H. Bao, M. Chen, Nonlinear Dyn. 89, 1157 (2017)

    Article  Google Scholar 

  12. K. Rajagopal, H. Jahanshahi, M. Varan, I. Bayr, V.-T. Pham, S. Jafari, A. Karthikeyan, AEU Int. J. Electron. Commun. 94, 55 (2018)

    Article  Google Scholar 

  13. S. Vaidyanathan, V.-T. Pham, C. Volos, Advances in memristors, memristive devices and systems (Springer, 2017), p. 101

  14. Y. Xu, Y. Jia, J. Ma, A. Alsaedi, B. Ahmad, Chaos Solitons Fractals 104, 435 (2017)

    Article  ADS  Google Scholar 

  15. Y. Xu, Y. Jia, J. Ma, T. Hayat, A. Alsaedi, Sci. Rep. 8, 1349 (2018)

    Article  ADS  Google Scholar 

  16. V. Berec, Eur. Phys. J. Special Topics 225, 7 (2016)

    Article  ADS  Google Scholar 

  17. M. Bolotov, L. Smirnov, G. Osipov, A. Pikovsky, Chaos 28, 045101 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  18. D. Dudkowski, Y. Maistrenko, T. Kapitaniak, Chaos 26, 116306 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  19. A. Yeldesbay, A. Pikovsky, M. Rosenblum, Phys. Rev. Lett. 112, 144103 (2014)

    Article  ADS  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

  22. B.K. Bera, S. Majhi, D. Ghosh, M. Perc, EPL 118, 10001 (2017)

    Article  ADS  Google Scholar 

  23. V. Berec, Chaos Solitons Fractals 86, 75 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  24. S. Brezetskiy, D. Dudkowski, P. Jaros, J. Wojewoda, K. Czolczynski, Y. Maistrenko, T. Kapitaniak, Indian Acad. Sci. Conf. Ser. 1, 187 (2017)

    Google Scholar 

  25. D. Dudkowski, Y. Maistrenko, T. Kapitaniak, Phys. Rev. E 90, 032920 (2014)

    Article  ADS  Google Scholar 

  26. Z. Faghani, Z. Arab, F. Parastesh, S. Jafari, M. Perc, M. Slavinec, Chaos Solitons Fractals 114, 306 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  27. J. Tang, J. Zhang, J. Ma, J. Luo, Sci. China Technol. Sci. 62, 1134 (2019)

    Article  Google Scholar 

  28. J.D. Hart, K. Bansal, T.E. Murphy, R. Roy, Chaos 26, 094801 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  29. S. Ghosh, A. Kumar, A. Zakharova, S. Jalan, EPL 115, 60005 (2016)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. S. Kundu, S. Majhi, B.K. Bera, D. Ghosh, M. Lakshmanan, Phys. Rev. E 97, 022201 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  32. T. Kapitaniak, P. Kuzma, J. Wojewoda, K. Czolczynski, Y. Maistrenko, Sci. Rep. 4 (2014)

  33. F. Parastesh, S. Jafari, H. Azarnoush, B. Hatef, A. Bountis, Chaos Solitons Fractals 110, 203 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  34. S.W. Haugland, L. Schmidt, K. Krischer, Sci. Rep. 5, 9883 (2015)

    Article  ADS  Google Scholar 

  35. S. Majhi, D. Ghosh, Chaos 28, 083113 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  36. A.V. Slepnev, A.V. Bukh, T.E. Vadivasova, Nonlinear Dyn. 88, 2983 (2017)

    Article  Google Scholar 

  37. Z. Wei, F. Parastesh, H. Azarnoush, S. Jafari, D. Ghosh, M. Perc, M. Slavinec, EPL 123, 48003 (2018)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  39. D. Dudkowski, K. Czołczyński, T. Kapitaniak, Nonlinear Dyn. 95, 1859 (2019)

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

  42. H. Bao, N. Wang, B. Bao, M. Chen, P. Jin, G. Wang, Commun. Nonlinear Sci. Numer. Simul. 57, 264 (2018)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran, 15875-4413, Iran

    Fatemeh Parastesh, Sajad Jafari & Hamed Azarnoush

Authors
  1. Fatemeh Parastesh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sajad Jafari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hamed Azarnoush
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sajad Jafari.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Parastesh, F., Jafari, S. & Azarnoush, H. Traveling patterns in a network of memristor-based oscillators with extreme multistability. Eur. Phys. J. Spec. Top. 228, 2123–2131 (2019). https://doi.org/10.1140/epjst/e2019-900021-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2019-900021-6

Search

Navigation