Dynamics of Three and Four Non-identical Josephson Junctions

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Authors

  • Alexander P. Kuznetsov Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov, 410019, Russian Federation Author
  • Igor R. Sataev Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov, 410019, Russian Federation Author
  • Yuliya V. Sedova Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov, 410019, Russian Federation Author

DOI:

https://doi.org/10.5890/JAND.2018.03.009

Abstract

Dynamics of chains of three and four coupled non-identical Josephson junctions is considered. Synchronization effects are discussed including resonance Arnold web formation on the base of tori of different dimensions.

References

[1] Pikovsky, A., Rosenblum, M., and Kurths, J. (2001), Synchronization. A Universal Concept in Nonlinear Sciences, Cambridge University Press.

[2] Wiesenfeld, K., Colet, P., and Strogatz, S.H. (1996), Synchronization transitions in a disordered Josephson series array, Phys. Rev. Lett., 76, 404–407.

[3] Valkering, T.P., Hooijer, C.L.A., and Kroon, M.F. (2000), Dynamics of two capacitively coupled Josephson junctions in the overdamped limit, Physica D: Nonlinear Phenomena, 135, 137–153.

[4] Vlasov, V. and Pikovsky, A. (2013), Synchronization of a Josephson junction array in terms of global variables, Phys. Rev. E, 88, 022908.

[5] Kuznetsov, S.P. (2016), From geodesic flow on a surface of negative curvature to electronic generator of robust chaos, Int. J. Bifurcation Chaos, 26, 1650232.

[6] Baesens, C., Guckenheimer, J., Kim, S., and MacKay, R.S. (1991), Three coupled oscillators: mode locking, global bifurcations and toroidal chaos, Physica D: Nonlinear Phenomena, 49, 387-475.

[7] Emelianova, Yu.P., Kuznetsov, A.P., Sataev, I.R., and Turukina, L.V. (2013), Synchronization and multifrequency oscillations in the low-dimensional chain of the self-oscillators, Physica D: Nonlinear Phenomena, 244, 36-49.

[8] Emelianova, Y.P., Kuznetsov, A.P., Turukina, L.V., Sataev, I.R., and Chernyshov, N.Yu. (2014), A structure of the oscillation frequencies parameter space for the system of dissipatively coupled oscillators, Communications in Nonlinear Science and Numerical Simulation, 19, 1203-1212.

[9] Benettin, G., Galgani, L., Giorgilli, A., and Strelcyn, J.-M. (1980), Lyapunov Characteristic Exponents for Smooth Dynamical Systems and for Hamiltonian Systems: A Method for Computing All of Them: P. 1: Theory; P. 2: Numerical Application, Meccanica, 15, 9-30.

[10] Hairer, E., Norsett., S.P., and Wanner, G. (1987), Solving Ordinary Differential Equations: 1. Nonstiff Problems, Berlin: Springer.

[11] Aronson, D.G., Ermentrout, G.B., and Kopell, N. (1990), Amplitude response of coupled oscillators, Physica D: Nonlinear Phenomena, 41, 403-449.

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PublishedMarch 2018

Usage tracking begins September 1, 2026.

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How to Cite

Kuznetsov, A. P., Sataev, I. R., & Sedova, Y. V. (2026). Dynamics of Three and Four Non-identical Josephson Junctions. Journal of Applied Nonlinear Dynamics, 7(1), 105-110. https://doi.org/10.5890/JAND.2018.03.009