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

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

 

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. [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.