Advertisement

Analysis of Oscillator Behavior Under Multi-frequency Excitation for Oscillatory Neural Networks

  • M. M. GouraryEmail author
  • S. G. Rusakov
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1126)

Abstract

Problems of the oscillator behavior under quasiperiodic multi-frequency excitation are considered in the paper. The new concept of the multi-frequency synchronization is proposed as the natural extension of the traditional synchronization concept for the periodically excited oscillator. Derived analytical expressions and performed simulation examples demonstrate the consistency of the proposed concept. The investigations are based on the modified Kuramoto model of a single oscillator under a narrowband quasiperiodic excitation. Analytical results are obtained by multiple timescales methods.

Keywords

Oscillators Kuramoto model Phase macromodels Synchronization Dynamical system Transfer factor 

Notes

Acknowledgements

The reported study was funded by RFBR, project number 19-29-03012.

References

  1. 1.
    Kharola, A.: Artificial neural networks based approach for predicting LVDT output characteristic. Int. J. Eng. Manuf. (IJEM) 8(4), 21–28 (2018).  https://doi.org/10.5815/ijem.2018.04.03CrossRefGoogle Scholar
  2. 2.
    Mohsen, A.A., Alsurori, M., Aldobai, B., Mohsen, G.A.: New approach to medical diagnosis using artificial neural network and decision tree algorithm: application to dental diseases. Int. J. Inf. Eng. Electron. Bus. (IJIEEB) 11(4), 52–60 (2019).  https://doi.org/10.5815/ijieeb.2019.04.06CrossRefGoogle Scholar
  3. 3.
    Gupta, D.K., Goyal, S.: Credit risk prediction using artificial neural network algorithm. Int. J. Mod. Educ. Comput. Sci. (IJMECS) 10(5), 9–16 (2018).  https://doi.org/10.5815/ijmecs.2018.05.02CrossRefGoogle Scholar
  4. 4.
    Kuzmina, M., Manykin, E., Grichuk, E.: Oscillatory neural networks. In: Problems of Parallel Information Processing, p. 160. Walter de Gruyter GmbH, Berlin/Boston (2014)Google Scholar
  5. 5.
    Hoppensteadt, F.C., Izhikevich, E.M.: Pattern recognition via synchronization in phase-locked loop neural networks. IEEE Trans. Neural Netw. 11(3), 734–738 (2000)CrossRefGoogle Scholar
  6. 6.
    Maffezzoni, P., Bahr, B., Zhang, Z., Daniel, L.: Oscillator array models for associative memory and pattern recognition. IEEE Trans. Circuits Syst. I Regul. Pap. 62(6), 1591–1598 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Bonnin, M., Corinto, F., Gilli, M.: Periodic oscillations in weakly connected cellular nonlinear networks. IEEE Trans. Circuits Syst. I Regul. Pap. 55(6), 1671–1684 (2008).  https://doi.org/10.1109/TCSI.2008.916460MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ashwin, P., Coombes, S., Nicks, R.: Mathematical frameworks for oscillatory network dynamics in neuroscience. J. Math Neurosci. 6(1), 2 (2016).  https://doi.org/10.1186/s13408-015-0033-6MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Bhansali, P., Roychowdhury, J.: Injection locking analysis and simulation of weakly coupled oscillator networks. In: Li, P., Silveira, L.M., Feldmann, P. (eds.) Simulation and Verification of Electronic and Biological Systems, pp. 71–93. Springer, Dordrecht (2011).  https://doi.org/10.1007/978-94-007-0149-6_4CrossRefGoogle Scholar
  10. 10.
    Kumar, P., Verma, D., Parmananda, P.: Partially synchronized states in an ensemble of chemo-mechanical oscillators. Phys. Lett. A. 381(29), 2337–2343 (2017).  https://doi.org/10.1016/j.physleta.2017.05.032CrossRefGoogle Scholar
  11. 11.
    Frolov, N.S., Goremyko, M.V., Makarov, V.V., Maksimenk, V.A., Hramov, A.E.: Numerical and analytical investigation of the chimera state excitation conditions in the Kuramoto-Sakaguchi oscillator network. In: Proceedings of SPIE 10063, Dynamics and Fluctuations in Biomedical Photonics XIV, 100631H (2017).  https://doi.org/10.1117/12.2251702
  12. 12.
    Asfar, K.R., Nayfeh, A.H., Mook, D.T.: Response of self-excite oscillation to multifrequency excitations. J. Sound Vib. 79(4), 589–604 (1981)CrossRefGoogle Scholar
  13. 13.
    El-Bassiouny, A.F.: Parametrically excited nonlinear systems: a comparison of two methods. Int. J. Math. Math. Sci. 32(12), 739–761 (2002).  https://doi.org/10.1155/S0161171202007019MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Malinowski, M., et al.: Towards on-chip self-referenced frequency-comb sources based on semiconductor mode-locked lasers. Micromachines 10(6), 391 (2019).  https://doi.org/10.3390/mi10060391CrossRefGoogle Scholar
  15. 15.
    Kuznetsov, A.P., Sataev, I.R., Tyuryukina, L.V.: Synchronization of quasi-periodic oscillations in coupled phase oscillators. Tech. Phys. Lett. 36(5), 478–481 (2010).  https://doi.org/10.1134/S1063785010050263CrossRefGoogle Scholar
  16. 16.
    Peleshchak, R., Lytvyn, V., Bihun, O., Peleshchak, I.: Structural transformations of incoming signal by a single nonlinear oscillatory neuron or by an artificial nonlinear neural network. Int. J. Intell. Syst. Appl. (IJISA) 11(8), 1–10 (2019).  https://doi.org/10.5815/ijisa.2019.08.01CrossRefGoogle Scholar
  17. 17.
    Acebrón, J.A., Bonilla, L.L., Vicente, C.J.P., Ritort, F., Spigler, R.: The Kuramoto model: a simple paradigm for synchronization phenomena. Rev. Mod. Phys. 77(1), 137–185 (2005).  https://doi.org/10.1103/RevModPhys.77.137CrossRefGoogle Scholar
  18. 18.
    Gourary, M.M., Rusakov, S.G.: Analysis of oscillator ensemble with dynamic couplings. In: Hu, Z., Petoukhov, S., He, M. (eds.) Advances in Artificial Systems for Medicine and Education II, AIMEE 2018. Advances in Intelligent Systems and Computing, vol. 902. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-12082-5_15CrossRefGoogle Scholar
  19. 19.
    Adler, R.: A study of locking phenomena in oscillators. Proc. IEEE 61(10), 1380–1385 (1973)CrossRefGoogle Scholar
  20. 20.
    Schilder, F., Vogt, W., Schreiber, S., Osinga, H.M.: Fourier methods for quasi-periodic oscillations. Int. J. Numer. Methods Eng. 67(5), 629–671 (2006)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Langella, R., Testa, A.: Amplitude and phase modulation effects of waveform distortion in power systems. Electr. Power Qual. Util. J. 13(1), 25–32 (2007)Google Scholar
  22. 22.
    Razavi, B.: A study of injection locking and pulling in oscillators. IEEE J. Solid-State Circuits 39(9), 1415–1424 (2004)CrossRefGoogle Scholar
  23. 23.
    Desroches, M., et al.: Mixed-mode oscillations with multiple time scales. SIAM Rev. 54(2), 211–288 (2012).  https://doi.org/10.1137/100791233MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute for Design Problems in Microelectronics of Russian Academy of Sciences (IPPM RAS)MoscowRussia

Personalised recommendations