Non-conventional Synchronization of Weakly Coupled Active Oscillators

  • Leonid I. ManevitchEmail author
  • Agnessa Kovaleva
  • Valeri Smirnov
  • Yuli Starosvetsky
Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)


In this chapter, we describe a new type of self-sustained oscillations associated with the phenomenon of synchronization. Conventional studies of synchronization in the model of two weakly coupled Van der Pol oscillators considered their synchronization in the regimes close to nonlinear normal modes (NNMs).


  1. Akhmediev, N.N., Ankiewicz, A.: Solitons: Nonlinear Pulses and Beams. Chapman & Hall, London (1997)zbMATHGoogle Scholar
  2. Chakraborty, T., Rand, R.H.: The transition from phase locking to drift in a system of two weakly coupled Van der Pol oscillators. Int. J. Nonlinear Mech. 23, 369–376 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  3. Kovaleva, M.A., Manevitch, L.I., Pilipchuk, V.N.: New type of synchronization for auto-generator with hard excitation. J. Exp. Theor. Phys. 116, 369–377 (2013)CrossRefGoogle Scholar
  4. Landa, P.S., Duboshinskiĭ, Ya.B.: Self-oscillatory systems with high-frequency energy sources. Sov. Phys. Usp. 32, 723 (1989)Google Scholar
  5. Landa, P.S.: Nonlinear Oscillations and Waves in Dynamical Systems. Kluwer Academic Publishers, Dordrecht (1996)CrossRefzbMATHGoogle Scholar
  6. Malomed, B.A.: Waves and solitary pulses in a weakly inhomogeneous Ginzburg-Landau equations. Phys. Rev. E 50, 4249–4252 (1994)MathSciNetCrossRefGoogle Scholar
  7. Manevitch, L.I., Kovaleva, M.A., Pilipchuk, V.N.: Non-conventional synchronization of weakly coupled active oscillators, Eur. Lett. 101, 50002 (1–5) (2013)Google Scholar
  8. Mihalache, D., Mazilu, D., Lederer, F., Kivshar, Y.S.: Spatiotemporal surface Ginzburg-Landau solitons. Phys. Rev. A 77, 043828 (1–6) (2008)Google Scholar
  9. Newell, A.C., Nazarenko, S., Biven, L.: Wave turbulence and intermittency. Physica D 152(153), 520–550 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  10. Ovsyannikov, L.V.: Group Analysis of Differential Equations. Academic Press, New York (1982)zbMATHGoogle Scholar
  11. Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press (2001)Google Scholar
  12. Rompala, K., Rand, R., Howland, H.: Dynamics of three coupled van der Pol oscillators, with application to circadian rhythms. Commun. Nonlinear Sci. Numer. Simul. 12, 794–803 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. Vakakis, A.F., Manevitch, L.I., Mikhlin, Y.V., Pilipchuk, V.N., Zevin, A.A.: Normal Modes and Localization in Nonlinear Systems. Wiley, New York (1996)CrossRefzbMATHGoogle Scholar
  14. Verhulst, F.: Invariant manifolds in dissipative dynamical systems. Acta Appl. Math. 87, 229–244 (2005)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Leonid I. Manevitch
    • 1
    Email author
  • Agnessa Kovaleva
    • 2
  • Valeri Smirnov
    • 1
  • Yuli Starosvetsky
    • 3
  1. 1.Institute of Chemical PhysicsRussian Academy of ScienceMoscowRussia
  2. 2.Space Research InstituteRussian Academy of ScienceMoscowRussia
  3. 3.Technion—Israel Institute of TechnologyFaculty of Mechanical EngineeringHaifaIsrael

Personalised recommendations