Skip Navigation Links
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Dynamics of Three and Four Non-identical Josephson Junctions

Journal of Applied Nonlinear Dynamics 7(1) (2018) 105--110 | DOI:10.5890/JAND.2018.03.009

Alexander P. Kuznetsov, Igor R. Sataev, Yuliya V. Sedova

Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov, 410019, Russian Federation

Download Full Text PDF



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.


  1. [1]  Pikovsky, A., Rosenblum, M., and Kurths, J. (2001), Synchronization. A Universal Concept in Nonlinear Sciences, Cambridge University Press.
  2. [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. [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. [4]  Vlasov, V. and Pikovsky, A. (2013), Synchronization of a Josephson junction array in terms of global variables, Phys. Rev. E, 88, 022908.
  5. [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. [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. [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. [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. [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. [10]  Hairer, E., Norsett., S.P., and Wanner, G. (1987), Solving Ordinary Differential Equations: 1. Nonstiff Problems, Berlin: Springer.
  11. [11]  Aronson, D.G., Ermentrout, G.B., and Kopell, N. (1990), Amplitude response of coupled oscillators, Physica D: Nonlinear Phenomena, 41, 403-449.