Skip to main content
SpringerLink
Log in

Enhancing the emergence of hyperchaos using an indirect coupling and its verification based on digital implementation

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this work, an indirect coupling used in a pair of simple autonomous discrete systems in order to enhance the emergence of hyperchaos is presented. The peculiarity that the used systems will never generate chaotic or hyperchaotic dynamics by itself makes this case an interesting problem to address. Moreover, it is possible to achieve in-phase or anti-phase synchronization by varying some parameters of the indirect coupling. Additionally, different methods to analyze the emerging dynamics of the coupled systems using an indirect coupling compared to a conventional coupling are presented. Finally, an electronic digital implementation is conducted by using the SPI protocol of two coupled PIC-24FJ64GA006 16-bit microcontrollers.

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

Similar content being viewed by others

Data availability

All data generated or analyzed during this study are included in this published article.

References

  1. Hai-Feng, Z., Rui-Xin, W., Xin-Chu, F.: The emergence of chaos in complex dynamical networks. Chaos Soliton Fract. 28(2), 472–479 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Fiordilino, E.: The emergence of chaos in quantum mechanics. Symmetry 12(5), 785 (2020)

    Article  Google Scholar 

  3. Plan, E.L.C.V.M., Musacchio, S., Vincenzi D.: Emergence of chaos in a viscous solution of rods. Phy. Rev. E 96, 053108 (2017)

  4. Andreev, A.V., Balanov, A.G., Fromhold, T.M., Greenaway, M.T., Hramov, A.E., Li, W., Makarov, V.V., Zagoskin, A.M.: Emergence and control of complex behaviors in driven systems of interacting qubits with dissipation. npj Quantum Inf. 7(1) (2021)

  5. Ghosh, A., Sujith, R.I.: Emergence of order from chaos: a phenomenological model of coupled oscillators. Chaos Soliton Fract. 141, 110334 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chun-Ni, W., Ma, J., Liu, Y., Huang, L.: Chaos control, spiral wave formation, and the emergence of spatiotemporal chaos in networked Chua circuits. Nonlinear Dyn. 67(1), 139–146 (2012)

    Article  MATH  Google Scholar 

  7. Van Gorder, R.A.: Emergence of chaotic regimes in the generalized Lorenz canonical form: a competitive modes analysis. Nonlinear Dyn. 66, 153–160 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Manjunath, S., Podapati, A., Raina, G.: Stability, convergence, limit cycles and chaos in some models of population dynamics. Nonlinear Dyn. 87(4), 2577–2595 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ulrichs, H., Mann, A., Parlitz, U.: Synchronization and chaotic dynamics of coupled mechanical metronomes. Chaos 19(4), 043120 (2009)

    Article  Google Scholar 

  10. Arellano-Delgado, A., López-Gutiérrez, R.M., Murillo-Escobar, M.A., Cardoza-Avendaño, L., Cruz-Hernández, C.: The Emergence of Hyperchaos and Synchronization in Networks with Discrete Periodic Oscillators. Entropy 19(8), 1–15 (2017)

    Article  MathSciNet  Google Scholar 

  11. Blasius, B., Huppert, A., Stone, L.: Complex Dynamics and Phase Synchronization in Spatially Extended Ecological Systems. Nature 399, 354–359 (1999)

    Article  Google Scholar 

  12. Strogatz, S.H.: Spontaneous synchronization in nature. In: Proceedings of International Frequency Control Symposium, pp. 2–4 (1997)

  13. Hyun-Ho, C., Jung-Ryun, L.: Principles, applications, and challenges of synchronization in nature for future mobile communication systems. Mob. Inf. Syst. 2017, 8932631 (2017)

    Google Scholar 

  14. Hale, J.K.: Diffusive coupling, dissipation, and synchronization. J. Dyn. Differ. Equ. 9, 1–52 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  15. Brauns, F., Halatek, J., Frey, E.: Diffusive coupling of two well-mixed compartments elucidates elementary principles of protein-based pattern formation. Phys. Rev. Res. 3, 013258 (2021)

    Article  Google Scholar 

  16. Van Quoc, T., Minh Hoang, T., Nam Hoai, N., Hyo-Sung, A.: Free-will arbitrary time consensus protocols with diffusive coupling. Int. J. Robust Nonlin. 32(15), 8711–8731 (2022)

    Article  MathSciNet  Google Scholar 

  17. Pena Ramirez, J., Arellano-Delgado, A., Nijmeijer, H.: Enhancing master-slave synchronization: The effect of using a dynamic coupling. Phys. Rev. E. 98(1), 012208 (2018)

    Article  Google Scholar 

  18. Arellano-Delgado, A., López-Gutiérrez, R.M., Méndez-Ramírez, R., Cardoza-Avendaño, L., Cruz-Hernández, C.: Dynamic coupling in small-world outer synchronization of chaotic networks. Phys. D 423, 132928 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  19. Pena Ramirez, J., Garcia, E., Alvarez, J.: Master-slave synchronization via dynamic control. Commun. Nonlinear Sci. 80, 104977 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  20. de Jonge, W., Pena Ramirez, j., Nijmeijer, H.: Dynamic coupling enhances network synchronization. IFAC Papers OnLine. 52(16), 610–615 (2019)

  21. Buscarino, A., Fortuna, L., Patanè, L.: Master-slave synchronization of hyperchaotic systems through a linear dynamic coupling. Phys. Rev. E 100, 032215 (2019)

    Article  Google Scholar 

  22. Rubio-Pecasso, J., López-Gutiérrez, R.M., Arellano-Delgado, A., Cruz-Hernández, C.: Quadcopter formation using backstepping control and dynamic coupling in master–slave configuration. In: 2022 International Conference on Control, Robotics and Informatics, pp. 2–4 (2022)

  23. Méndez-Ramírez, R.D., Arellano-Delgado, A., Murillo-Escobar, M.A., Cruz-Hernández, C.: A New 4D Hyperchaotic System and Its Analog and Digital Implementation. Electronics 10(15), 1793 (2021)

    Article  Google Scholar 

  24. Méndez-Ramírez, R.D., Arellano-Delgado, A., Murillo-Escobar, M.A., Cruz-Hernandez, C.: A new 4D hyperchaotic system and its analog and digital implementation. Electronics 10(15), 1793 (2021)

    Article  Google Scholar 

  25. Tlelo-Cuautle, E., Carbajal-Gomez, V.H., Obeso-Rodelo, P.J. Rangel-Magdaleno., J. J. Núñez-Pérez J. C.: FPGA realization of a chaotic communication system applied to image processing. Nonlinear Dyn. 82, 1879–1892 (2015)

  26. Bonny, T., Nasir, Q.: Clock glitch fault injection attack on an FPGA-based non-autonomous chaotic oscillator. Nonlinear Dyn. 96, 2087–2101 (2019)

    Article  Google Scholar 

  27. Rodríguez-Orozco, E., García-Guerrero, E.E., Inzunza-Gonzalez, E., López-Bonilla, O.R., Flores-Vergara, A., Cárdenas-Valdez, J.R., Tlelo-Cuautle, E.: FPGA-based chaotic cryptosystem by using voice recognition as access key. Electronics 7, 414 (2018)

    Article  MATH  Google Scholar 

  28. Benkouider, K., Vaidyanathan, S., Sambas, A., Tlelo-Cuautle, E., El-Latif, A.A.A., Abd-El-Atty, B., Bermudez-Marquez, C.F., Sulaiman, I.M., Awwal, A.M., Kumam, P.: A New 5-D multistable hyperchaotic system with three positive lyapunov exponents: bifurcation analysis, circuit design, FPGA realization and image encryption. IEEE Access. 10(22014271), 90111–90132 (2022)

    Article  Google Scholar 

  29. Leng, X., Du, B., Gu, S., He, S.: Novel dynamical behaviors in fractional-order conservative hyperchaotic system and DSP implementation. Nonlinear Dyn. 109, 1167–1186 (2022)

    Article  Google Scholar 

  30. Liu, T., Yan, H., Banerjee, S., Mou, J.: A fractional-order chaotic system with hidden attractor and self-excited attractor and its DSP implementation. Chaos Soliton Fract. 145, 110791 (2021)

    Article  MathSciNet  Google Scholar 

  31. Ma, C., Mou, J., Cao, Y., Liu, T., Wang, J.: Multistability analysis of a conformable fractional-order chaotic system. Phys. Scr. 95(7), 075204 (2020)

    Article  Google Scholar 

  32. Ponomarenko, V.I., Prokhorov, M.D., Karavaev, A.S., Kulminskiy, D.D.: An experimental digital communication scheme based on chaotic time-delay system. Nonlinear Dyn. 74, 1013–1020 (2013)

    Article  MathSciNet  Google Scholar 

  33. Trujillo-Toledo, D.A., López-Bonilla, O.R., García-Guerrero, E.E., Tlelo-Cuautle, E., López-Mancilla, D., Guillén-Fernández, O., Inzunza-González, E.: Real-time RGB image encryption for IoT applications using enhanced sequences from chaotic maps. Chaos Soliton Fract. 153(2), 111506 (2021)

    Article  MathSciNet  Google Scholar 

  34. Giakoumis, A.E., Volos, C.K., Stouboulos, I.N., Polatoglou, H.M., Kyprianidis, I.M.: Chaos generator device based on a 32 bit microcontroller embedded system. In: 2018 7th International Conference on Modern Circuits and Systems Technologies, pp. 1–4 (2018)

  35. Vathakkattil, G., Vikram Pakrashi, J.: Limits on anti-phase synchronization in oscillator networks. Sci. Rep. 10, 10178 (2020)

    Article  Google Scholar 

  36. Rui Dilão.: Antiphase and in-phase synchronization of nonlinear oscillators: The Huygens’s clocks system. Chaos 19, 023118 (2009)

  37. Wolf, P.A., Swift, J.B., Swinney, H.L., VastanoJ, A.: Determining Lyapunov exponents from a time series. Phys. D 16, 285 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  38. Méndez-Ramírez, R.D., Arellano-Delgado, A., Murillo-Escobar, M.A., Cruz-Hernández, C.: Degradation analysis of chaotic systems and their digital implementation in embedded systems. Complexity 2019, 9863982 (2019)

    Article  Google Scholar 

Download references

Acknowledgements

This research was funded by CONACYT through the Research Project on Basic Science, ref. 166654 (A1-S-31628). A. Arellano-Delgado is a CONACYT ResearchFellow commissioned to the Universidad Autónoma de Baja California (Project no. 3059).

Author information

Author notes

  1. Rodrigo Daniel Méndez-Ramírez, Rosa Martha López-Gutiérrez, Miguel Angel Murillo-Escobar and Céesar Cruz-Hernández have contributed equally to this work.

Authors and Affiliations

  1. National Council of Science and Technology, Mexico City, 03940, Mexico

    Adrian Arellano-Delgado

  2. Electronics and Telecommunication Department, Scientific Research and Advanced Studies Center of Ensenada, 22860, Ensenada, BC, Mexico

    Rodrigo Daniel Méndez-Ramírez, Miguel Angel Murillo-Escobar & César Cruz-Hernández

  3. Engineering, Architecture and Design Faculty, Autonomous University of Baja California, 22860, Ensenada, BC, Mexico

    Adrian Arellano-Delgado, Rosa Martha López-Gutiérrez & Miguel Angel Murillo-Escobar

Authors
  1. Adrian Arellano-Delgado
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rodrigo Daniel Méndez-Ramírez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rosa Martha López-Gutiérrez
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Miguel Angel Murillo-Escobar
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. César Cruz-Hernández
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to César Cruz-Hernández.

Ethics declarations

Conflict of interest

Authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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

Arellano-Delgado, A., Méndez-Ramírez, R.D., López-Gutiérrez, R.M. et al. Enhancing the emergence of hyperchaos using an indirect coupling and its verification based on digital implementation. Nonlinear Dyn 111, 9591–9605 (2023). https://doi.org/10.1007/s11071-023-08313-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-08313-0

Keywords

Search

Navigation