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Experimental investigation of amplitude death in delay-coupled double-scroll circuits with randomly time-varying network topology

  • Shinnosuke Masamura
  • Tetsu Iwamoto
  • Yoshiki SugitaniEmail author
  • Keiji Konishi
  • Naoyuki Hara
Original paper
  • 32 Downloads

Abstract

The present study experimentally investigates amplitude death in delay-coupled double-scroll circuits with a time-varying network topology that randomly changes at a regular interval. Circuit experiments show that amplitude death can occur in the time-varying network. Furthermore, the experimental results well agree with the analytical results obtained based on a time-averaged adjacency matrix when the interval is much shorter than the natural period of the double-scroll circuits.

Keywords

Amplitude death Delayed coupling Time-varying network topology 

Notes

Acknowledgements

The present study was partially supported by JSPS KAKENHI (JP 26289131, JP 18H03306, and JP 17K12748).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

References

  1. 1.
    Masamura, S., Sugitani, Y., Konishi, K., Hara, N.: Experimental observation of amplitude death in a delay-coupled circuit network with fast time-varying network topology. In: Proceedings of the 2015 International Symposium on Nonlinear Theory and its Applications, pp. 357–360 (2015)Google Scholar
  2. 2.
    Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization. Cambridge University Press, Cambridge (2001)zbMATHCrossRefGoogle Scholar
  3. 3.
    Pecora, L.M., Carroll, T.L.: Master stability functions for synchronized coupled systems. Phys. Rev. Lett. 80, 2109–2112 (1998)CrossRefGoogle Scholar
  4. 4.
    Strogatz, S.: Sync: The Emerging Science of Spontaneous Order. Hachette Books, New York (2003)Google Scholar
  5. 5.
    Resmi, V., Ambika, G., Amritkar, R.E.: General mechanism for amplitude death in coupled systems. Phys. Rev. E 84, 046212 (2011)CrossRefGoogle Scholar
  6. 6.
    Saxena, G., Prasad, A., Ramaswamy, R.: Amplitude death: the emergence of stationarity in coupled nonlinear systems. Phys. Rep. 521, 205–228 (2012)CrossRefGoogle Scholar
  7. 7.
    Koseska, A., Volkov, E., Kurths, J.: Oscillation quenching mechanisms: amplitude vs. oscillation death. Phys. Rep. 531, 173–199 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Prasad, A.: Amplitude death in coupled chaotic oscillators. Phys. Rev. E 72, 056204 (2005)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Amitai, E., Koppenhöfer, M., Lörch, N., Bruder, C.: Quantum effects in amplitude death of coupled anharmonic self-oscillators. Phys. Rev. E. 97, 052203 (2018)CrossRefGoogle Scholar
  10. 10.
    Sun, Z., Xiao, R., Yang, X., Xu, W.: Quenching oscillating behaviors in fractional coupled Stuart–Landau oscillators. Chaos 28, 033109 (2018)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Xiao, R., Sun, Z., Yang, X., Xu, W.: Amplitude death islands in globally delay-coupled fractional-order oscillators. Nonlinear Dyn. 95, 2093–2102 (2019)CrossRefGoogle Scholar
  12. 12.
    Teki, H., Konishi, K., Hara, N.: Amplitude death in a pair of one-dimensional complex Ginzburg-Landau systems coupled by diffusive connections. Phys. Rev. E. 95, 062220 (2017)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Van Gorder, R.A., Krause, A.L., Kwiecinski, J.A.: Amplitude death criteria for coupled complex Ginzburg-Landau systems. Nonlinear Dyn. 97, 151–159 (2019)CrossRefGoogle Scholar
  14. 14.
    Sharma, A.: Time delay induced partial death patterns with conjugate coupling in relay oscillators. Phys. Lett. A. 383, 1865–1870 (2019)CrossRefGoogle Scholar
  15. 15.
    Wei, D.Q., Zhang, B., Luo, X.S., Zeng, S.Y., Qiu, D.Y.: Effects of couplings on the collective dynamics of permanent-magnet synchronous motors. IEEE Trans. Circuits Syst. 60, 692–696 (2013)CrossRefGoogle Scholar
  16. 16.
    Huddy, S.R., Skufca, J.D.: Amplitude death solutions for stabilization of dc microgrids with instantaneous constant-power loads. IEEE Trans. Power Electron. 28, 247–253 (2013)CrossRefGoogle Scholar
  17. 17.
    Subudhi, S.K., Maity, S.: Effect of heterogeneity on amplitude death based stability solution of DC microgrid. In: Proceedings of 2018 International Conference on Power, Instrumentation, Control and Computing, pp. 1–5 (2018)Google Scholar
  18. 18.
    Biwa, T., Tozuka, S., Yazaki, T.: Amplitude death in coupled thermoacoustic oscillators. Phys. Rev. Appl. 3, 034006 (2015)CrossRefGoogle Scholar
  19. 19.
    Hyodo, H., Biwa, T.: Stabilization of thermoacoustic oscillators by delay coupling. Phys. Rev. E. 98, 052223 (2018)CrossRefGoogle Scholar
  20. 20.
    Thomas, N., Mondal, S., Pawar, S.A., Sujith, R.I.: Effect of time-delay and dissipative coupling on amplitude death in coupled thermoacoustic oscillators. Chaos 28, 033119 (2018)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Bar-Eli, K.: On the stability of coupled chemical oscillators. Phys. D 14, 242–252 (1985)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Aronson, D.G., Ermentrout, G.B., Kopell, N.: Amplitude response of coupled oscillators. Phys. D 41, 403–449 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Reddy, D.V., Sen, A., Johnston, G.L.: Time delay induced death in coupled limit cycle oscillators. Phys. Rev. Lett. 80, 5109–5112 (1998)CrossRefGoogle Scholar
  24. 24.
    Reddy, D.V., Sen, A., Johnston, G.L.: Time delay effect on coupled limit cycle oscillators at Hopf bifurcation. Phys. D 129, 15–34 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Konishi, K., Hara, N.: Topology-free stability of a steady state in network systems with dynamic connections. Phys. Rev. E 83, 036204 (2011)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Karnatak, R., Ramaswamy, R., Prasad, A.: Amplitude death in the absence of time delays in identical coupled oscillators. Phys. Rev. E 76, 035201 (2007)CrossRefGoogle Scholar
  27. 27.
    Banerjee, T., Ghosh, D.: Transition from amplitude to oscillation death under mean-field diffusive coupling. Phys. Rev. E 89, 052912 (2014)CrossRefGoogle Scholar
  28. 28.
    Ghosh, D., Banerjee, T.: Transitions among the diverse oscillation quenching states induced by the interplay of direct and indirect coupling. Phys. Rev. E 90, 062908 (2014)CrossRefGoogle Scholar
  29. 29.
    Strogatz, S.H.: Death by delay. Nature 394, 316–317 (1998)CrossRefGoogle Scholar
  30. 30.
    Song, X., Wang, C., Ma, J., Tang, J.: Transition of electric activity of neurons induced by chemical and electric autapses. Sci. China Tech. Sci. 58, 1007–1014 (2015)CrossRefGoogle Scholar
  31. 31.
    Ma, J., Qin, H., Song, X., Chu, R.: Pattern selection in neuronal network driven by electric autapses with diversity in time delays. Int. J. Mod. Phys. B 29(1), 1450239 (2015)CrossRefGoogle Scholar
  32. 32.
    Ma, J., Tang, J.: A review for dynamics of collective behaviors of network of neurons. Sci. China Tech. Sci. 58, 2038–2045 (2015)CrossRefGoogle Scholar
  33. 33.
    Gjurchinovski, A., Zakharova, A., Schöll, E.: Amplitude death in oscillator networks with variable-delay coupling. Phys. Rev. E 89, 032915 (2014)CrossRefGoogle Scholar
  34. 34.
    Cakan, C., Lehnert, J., Schöll, E.: Heterogeneous delays in neural networks. Eur. Phys. J. B 87, 54 (2014)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Sugitani, Y., Konishi, K., Hara, N.: Delay-and topology-independent design for inducing amplitude death on networks with time-varying delay connections. Phys. Rev. E 92, 042928 (2015)CrossRefGoogle Scholar
  36. 36.
    Camp, T., Boleng, J., Davies, V.: A survey of mobility models for ad hoc network research. Wirel. Commun. Mob. Comput. 2, 483–502 (2002)CrossRefGoogle Scholar
  37. 37.
    Bashan, A., Bartsch, R.P., Kantelhardt, J.W., Havlin, S., Ivanov, P.C.: Network physiology reveals relations between network topology and physiological function. Nat. Commun. 3, 702 (2012)CrossRefGoogle Scholar
  38. 38.
    Calhoun, V.D., Miller, R., Pearlson, G., Adalı, T.: The chronnectome: time-varying connectivity networks as the next frontier in fMRI data discovery. Neuron 84, 262–274 (2014)CrossRefGoogle Scholar
  39. 39.
    González, M.C., Herrmann, H.J.: Scaling of the propagation of epidemics in a system of mobile agents. Phys. A 340, 741–748 (2004)CrossRefGoogle Scholar
  40. 40.
    Lèbre, S., Becq, J., Devaux, F., Stumpf, M.P.H., Lelandais, G.: Statistical inference of the time-varying structure of gene-regulation networks. BMC Syst. Biol. 4, 130 (2010)CrossRefGoogle Scholar
  41. 41.
    Sugitani, Y., Konishi, K., Hara, N.: Amplitude death in oscillators network with a fast time-varying network topology. In: Proceedings of Communications in Computer and Information Science vol. 438, 219–226 (2014)Google Scholar
  42. 42.
    Matsumoto, T., Chua, L., Komuro, M.: The double scroll. IEEE Trans. Circuits Syst. 32, 797–818 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  43. 43.
    Sawicki, J., Omelchenko, I., Zakharova, A., Schöll, E.: Chimera states in complex networks: interplay of fractal topology and delay. Eur. Phys. J. Spec. Top. 226, 1883–1892 (2017)CrossRefGoogle Scholar
  44. 44.
    Sugitani, Y., Konishi, K., Hara, N.: Experimental verification of amplitude death induced by a periodic time-varying delay-connection. Nonlinear Dyn. 70, 2227–2235 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  45. 45.
    Kennedy, M.P.: Robust OP amp realization of Chua’s circuit. Frequenz 46, 11 (1992)CrossRefGoogle Scholar
  46. 46.
    Stilwell, D.J., Bollt, E.M., Roberson, D.G.: Sufficient conditions for fast switching synchronization in time-varying network topologies. SIAM J. Appl. Dyn. Syst. 5, 140–156 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  47. 47.
    Porfiri, M., Stilwell, D.J., Bollt, E.M.: Synchronization in random weighted directed networks. IEEE Trans. Circuits Syst. 55, 3170–3177 (2008)MathSciNetCrossRefGoogle Scholar
  48. 48.
    Belykh, I.V., Belykh, V.N., Hasler, M.: Blinking model and synchronization in small-world networks with a time-varying coupling. Phys. D 195, 188–206 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  49. 49.
    Michiels, W., Niculescu, S.: Stability, Control, and Computation for Time-Delay Systems. Society for Industrial and Applied Mathematics, Philadelphia (2014)zbMATHCrossRefGoogle Scholar
  50. 50.
    Munoz-Pacheco, J.M., Zambrano-Serrano, E., Volos, C., Jafari, S., Kengne, J., Rajagopal, K.: A new fractional-order chaotic system with different families of hidden and self-excited attractors. Entropy 20, 564 (2018)CrossRefGoogle Scholar
  51. 51.
    Chaudhuri, U., Prasad, A.: Complicated basins and the phenomenon of amplitude death in coupled hidden attractors. Phys. Lett. A 378, 713–718 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  52. 52.
    Bhowmick, S.K., Amritkar, R.E., Dana, S.K.: Experimental evidence of synchronization of time-varying dynamical network. Chaos 22, 023105 (2012)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2020

Authors and Affiliations

  1. 1.Department of Electrical and Information SystemsOsaka Prefecture UniversityOsakaJapan
  2. 2.Department of Electrical and Electronic Systems EngineeringIbaraki UniversityIbarakiJapan

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