Skip to main content
SpringerLink
Log in

On the behavior of bidirectionally coupled multistable systems

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

Abstract

In this work, we study the synchronization states for a specific pair of mutually coupled multistable scroll systems. First, we determine conditions in the coupling scheme, to achieve partial or complete synchronization, under a uniform-coupling strength. Second, it is analyzed how the changes in the coupling strength modify the synchronous state. Our main results show that the nature of the coupling scheme determines the obtained synchronization type, while the coupling strength allows us to have various synchronized state attractors that differ from initial attractors. The analysis of the emergence of stable collective behavior is presented using Lyapunov functions of the different couplings and illustrated by numerical simulations.

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

Similar content being viewed by others

References

  1. U.. Feudel, Int. J. Bifurc. Chaos 18, 1607–1626 (2008)

    Article  MathSciNet  Google Scholar 

  2. A. Anzo-Hernández, H.E. Gilardi-Velázquez, E. Campos-Cantón, Chaos Interdiscip. J. Nonlinear Sci. 28, 033613 (2018)

    Article  Google Scholar 

  3. H.E. Gilardi-Velázquez, R. de Jesús Escalante-González, E. Campos-Cantón, IFAC PapersOnLine 51, 502–507 (2018)

  4. H.E. Gilardi-Velázquez, R.J. Escalante-González, E. Campos, Eur. Phys. J. Spec. Top. 229, 1351–1360 (2020)

    Article  Google Scholar 

  5. A.N. Pisarchik, U. Feudel, Phys. Rep. 540, 167–218 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  6. Z. Song, X. Jian, J. Theor. Biol. 313, 98–114 (2012)

    Article  ADS  Google Scholar 

  7. S.D. Glyzin, M.M. Preobrazhenskaia, IFAC-PapersOnLine 52, 109–114 (2019)

    Article  Google Scholar 

  8. L. Rürup, B. Mathes, C. Schmiedt-Fehr, A.S. Wienke, A. Özerdem, A. Brand, C. Basar-Eroglu, Int. J. Psychophysiol. 155, 127–139 (2020)

    Article  Google Scholar 

  9. A. Pikovsky, J. Kurths, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, vol. 12 (Cambridge University Press, Cambridge, 2003)

    Book  Google Scholar 

  10. A.N. Pisarchik, R. Jaimes-Reátegui, J.H. García-López, Int. J. Bifurc. Chaos 18, 1801–1819 (2008)

    Article  Google Scholar 

  11. L.M. Pecora, T.L. Carroll, Choas Interdiscip. J. Nonlinear Sci. 25, 097611 (2015)

    Article  Google Scholar 

  12. N.F. Rulkov, M.M. Sushchik, L.S. Tsimring, H.D.I. Abarbanel, Phys. Rev. E 51, 980 (1995)

    Article  ADS  Google Scholar 

  13. S. Boccaletti, J. Kurths, G. Osipov, D.L. Valladares, C.S. Zhou, Phys. Rep. 366, 1–101 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  14. A.N. Pisarchik, R. Jaimes-Reátegui, J.R. Villalobos-Salazar, J.H. Garcia-Lopez, S. Boccaletti, Phys. Rev. Lett. 96, 244102 (2006)

    Article  ADS  Google Scholar 

  15. R. Sevilla-Escoboza, J.M. Buldú, A.N. Pisarchik, S. Boccaletti, R. Gutiérrez, Phys. Rev. E 91, 032902 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  16. A. Anzo-Hernández, E. Campos-Cantón, M. Nicol, Commun. Nonlinear Sci. Numer. Simul. 70, 102–124 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  17. A. Ruiz-Silva, H.E. Gilardi-Velázquez, E. Campos, Chaos Solitons Fractals 151, 111263 (2021)

    Article  Google Scholar 

  18. H.E. Gilardi-Velázquez, L.J. Ontañón-García, D.G. Hurtado-Rodriguez, E. Campos-Cantón, Int. J. Bifurc. Chaos 27, 1730031 (2017)

    Article  Google Scholar 

  19. J.L. Echenausía-Monroy, G. Huerta-Cuellar, R. Jaimes-Reátegui, J.H. García-López, V. Aboites, B.B. Cassal-Quiroga, H.E. Gilardi-Velázquez, Electronics 9, 880 (2020)

    Article  Google Scholar 

  20. E. Campos-Cantón, J.G. Barajas-Ramirez, G. Solis-Perales, R. Femat, Chaos Interdiscip. J. Nonlinear Sci. 20, 013116 (2010)

    Article  Google Scholar 

  21. E. Campos-Cantón, R. Femat, G. Chen, Chaos Interdiscip. J. Nonlinear Sci. 22, 033121 (2012)

    Article  Google Scholar 

  22. Eric Campos-Cantón, Int. J. Mod. Phys. C 27, 1650008 (2016)

    Article  ADS  Google Scholar 

  23. G. Huerta-Cuellar, E. Jimenez-Lopez, E. Campos-Cantón, A.N. Pisarchik, Commun. Nonlinear Sci. Numer. Simul. 19, 2740–2746 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  24. H.E. Gilardi-Velázquez, E. Campos-Cantón, Int. J. Mod. Phys. C 29, 1850020 (2018)

    Article  ADS  Google Scholar 

  25. X.F. Wang, G. Chen, IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 49, 54–62 (2002)

    Article  Google Scholar 

  26. J. Lü, Y. Xinghuo, G. Chen, Phys. A 334, 281–302 (2004)

    Article  MathSciNet  Google Scholar 

  27. A.Y. Pogromsky, Chaos Interdiscip. J. Nonlinear Sci. 18, 037107 (2008)

    Article  Google Scholar 

  28. G. Chen, Int. J. Control Autom. Syst. 12, 221–230 (2014)

    Article  Google Scholar 

  29. T.-L. Liao, Shin-Hwa. Tsai, Chaos Solitons Fractals 11, 1387–1396 (2000)

    Article  ADS  Google Scholar 

  30. Z. Li, Z. Zhang, in 2011 International Conference on Electronics, Communications and Control (ICECC), (IEEE2011), pp. 2272–2275

  31. S. Celikovsky, G. Chen, IEEE Trans. Autom. Control 50, 76–82 (2005)

    Article  Google Scholar 

  32. A. Stefański, Tomasz Kapitaniak, Int. J. Solids Struct. 40, 5175–5185 (2003)

    Article  Google Scholar 

  33. T. Yang, L.O. Chua, IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 44, 976–988 (1997)

    Article  Google Scholar 

  34. A.D. Pano-Azucena, J. de Jesus Rangel-Magdaleno, E. Tlelo-Cuautle, A. de Jesus Quintas-Valles, Nonlinear Dyn. 87, 2203–2217 (2017)

  35. L. Keuninckx, M.C. Soriano, I. Fischer, C.R. Mirasso, R.M. Nguimdo, G. Van der Sande, Sci. Rep. 7, 43428 (2017)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

A.R.S. acknowledges CONACYT for the financial support to the realization of a post-doctoral stay in the University of Sonora (CVU-424195). H.E.G.V. acknowledges to PRODEP for the support (project 252787) to the realization of a post-doctoral stay in the University of Guadalajara, CULagos. G.H.C. acknowledges E.C.C. for fruitful discussions and the opportunity of the scientific stay at IPICYT.

Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Sonora, 83000, Hermosillo, Sonora, Mexico

    A. Ruiz-Silva

  2. Facultad de Ingeniería, Universidad Panamericana, Josemaría Escrivá de Balaguer 101, 20290, Aguascalientes, Aguascalientes, Mexico

    B. B. Cassal-Quiroga & H. E. Gilardi-Velázquez

  3. Dynamical Systems Laboratory, CULagos, Universidad de Guadalajara, Centro Universitario de los Lagos, Enrique Díaz de León 1144, Paseos de la Montaña, 47460, Lagos de Moreno, Jalisco, Mexico

    G. Huerta-Cuellar & H. E. Gilardi-Velázquez

Authors
  1. A. Ruiz-Silva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. B. Cassal-Quiroga
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Huerta-Cuellar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H. E. Gilardi-Velázquez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. E. Gilardi-Velázquez.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ruiz-Silva, A., Cassal-Quiroga, B.B., Huerta-Cuellar, G. et al. On the behavior of bidirectionally coupled multistable systems. Eur. Phys. J. Spec. Top. 231, 369–379 (2022). https://doi.org/10.1140/epjs/s11734-021-00406-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-021-00406-4

Search

Navigation