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Dynamics of a chain of unidirectionally coupled non-identical Van der Pol oscillators with a sinusoidal input at the first node

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Abstract

This paper investigates the dynamics of a chain of unidirectionally coupled non-identical Van der Pol (VdP) oscillators driven by a sinusoidal signal at the first node. Starting with a random generation of frequencies in the chain of standard VdP systems, we numerically study the influence of a small and a large value of disorder. It can be seen that disorder reduces the signal amplitude propagating along the chain and induces a coexistence of different dynamical states, namely periodic, quasiperiodic and chaotic states in the chain, which tend to disappear by suitably adjusting the coupling strength. A mathematical justification of the obtained dynamics is provided using multiple time-scale methods. Taking into account the cubic nonlinearity, the chain remains more or less coherent, no generation of the plateau of amplitude is observed for large disorder and the signal amplitude fluctuates greatly along the chain. Considering a chirp distribution of frequencies, the signal amplitude is characterised by a parabolic decrease followed by an irregular series of jumps back to a certain value. These effects are largely reduced by a moderate coupling strength and the presence of cubic nonlinearity.

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References

  1. S Boccaletti, N P Alexander, I G Charo and A Andreas, Synchronization: From coupled systems to complex networks (Cambridge University Press, 2018)

    Book  MATH  Google Scholar 

  2. E V Grigoryeva and S A Kaschenko, Appl. Nonlinear Dyn. 30, 189 (2022)

    Google Scholar 

  3. X Wei, H Zhang, Y Ding and J Ren, Sensors Actuators A: Phys. 304, 111904 (2020)

    Article  Google Scholar 

  4. H Peng and W Jun, IEEE Trans. Neural Networks Learning Syst. 30, 1672 (2018)

    Article  Google Scholar 

  5. A Saha and S Chakraverty, Natl Acad. Sci., India Sect. A: Phys. Sci. 91, 201 (2021)

    Google Scholar 

  6. M V Tchakui and P Woafo, Chaos 26, 113108 (2016)

    Article  ADS  Google Scholar 

  7. M V Tchakui, V Y Taffoti and P Woafo, Nonlinear Dyn. 84, 1961 (2016)

    Article  Google Scholar 

  8. J A Judge, B H Houston, D M Photiadis, P C Herdic, J A Judge, B H Houston, D M Photiadis and P C Herdic, J. Sound Vib. 290, 1119 (2006)

    Article  ADS  Google Scholar 

  9. Y Wang, L Wang, H Fan and X Wang, Chaos 29, 093118 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  10. Y Zhang, J L Ocampo-Espindola, I Z Kiss and A E Motter, Natl Acad. Sci. 118, e2024299118 (2021)

  11. Y Braiman, W Ditto, K Wiesenfeld and M Spano, Phys. Lett. A 206, 54 (1995)

    Article  ADS  Google Scholar 

  12. S F Brandt, B K Dellen and R Wessel, Phys. Rev. Lett. 96, 034104 (2006)

    Article  ADS  Google Scholar 

  13. D D Kulminskiy, V I Ponomarenko, M D Prokhorov and A E Hramov, Nonlinear Dyn. 98, 735 (2019)

    Article  Google Scholar 

  14. Z G Nicolaou, D Eroglu and A E Motter, Phys. Rev. X 9, 011017 (2019)

    Google Scholar 

  15. M V Tchakui, P Colet and P Woafo, Eur. Phys. J. B 92, 1 (2019)

    Article  Google Scholar 

  16. M V Tchakui, P Woafo, D Gomila and P Colet, Eur. Phys. J. Plus 137,1 (2022)

    Article  Google Scholar 

  17. K O Menzel, O Arp and A Piel, Phys. Rev. E 84, 016405 (2011)

    Article  ADS  Google Scholar 

  18. M Sinha, F Dorfler, B Johnson and S Dhople, IEEE 56th Annual Allerton Conference on Communication, Control and Computing (2018)

  19. P Woafo and H G Enjieu Kadji, Phys. Rev. E 69, 046206 (2004)

    Article  ADS  Google Scholar 

  20. K Fujii, S Hashimoto, Y Uwate and Y Nishio, IEEE Int. SoC Design Conf. (2018) pp. 164–165

  21. T Isozaki, T Nara, Y Uwate and Y Nishio, IEEE Int. SoC Design Conf. (2020) pp. 187–188

  22. F D Youmbi, E D Dongmo and P Woafo, Chaos Solitons Fractals 146, 110848 (2021)

    Article  Google Scholar 

  23. C Liu, Q Chen and J Zhang, IEEE Chin. Control Decision Conf. (2009) pp. 3677–3682

  24. A C de Pina Filho, M S Dutra and L S Raptopoulos, Biol. Cybernet. 92, 1 (2005)

  25. R Fonkou, P Louodop and P Kisito Talla, Phys. Scr. 97, 025001 (2022)

  26. J Kadmon and H Sompolinsky, Phys. Rev. X 5, 041030 (2015)

    Google Scholar 

  27. I Bashkirtseva, V Nasyrova and L Ryashko, Commun. Nonlinear Sci. Numer. Simul. 63, 261 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  28. C Hayashi, Nonlinear oscillations in physical systems (McGraw Hill, New York, 1964)

    MATH  Google Scholar 

  29. A H Nayfeh and D T Mook, Nonlinear oscillations (John Wiley and Sons, 1979)

    MATH  Google Scholar 

  30. J C Chedjou, H B Fotsin and P Woafo, Phys. Scr. 55, 390 (1997)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the i-COOP program of the Spanish Consejo Superior de Investigaciones Científicas, Grant Number COOPB20476. M V Tchakui wishes to acknowledge the support of the African–German Network of Excellence in Science (AGNES) under the AGNES-PAWS Grant.

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, National Higher Polytechnic Institute, University of Bamenda, P.O. Box 39, Bamenda, Cameroon

    Murielle Vanessa Tchakui

  2. Lab. Modelling and Simulation in Engineering, Biomimetics and Prototypes, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

    Murielle Vanessa Tchakui & Paul Woafo

  3. IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, 07122, Palma de Mallorca, Spain

    Murielle Vanessa Tchakui, Damia Gomila & Pere Colet

  4. Laboratory of Products Development and Entrepreneurship, Institut Supérieur de l’Innovation et de Technologie, P.O. Box 8210, Yaoundé, Cameroon

    Murielle Vanessa Tchakui & Paul Woafo

Authors
  1. Murielle Vanessa Tchakui
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  2. Paul Woafo
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  3. Damia Gomila
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  4. Pere Colet
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Correspondence to Murielle Vanessa Tchakui.

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Tchakui, M.V., Woafo, P., Gomila, D. et al. Dynamics of a chain of unidirectionally coupled non-identical Van der Pol oscillators with a sinusoidal input at the first node. Pramana - J Phys 97, 126 (2023). https://doi.org/10.1007/s12043-023-02609-x

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  • DOI: https://doi.org/10.1007/s12043-023-02609-x

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