ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Ryskin N. M., Usacheva S. A. Synchronization of periodic oscillation in a delayed-feedback oscillator by external harmonic driving. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 1, pp. 3-12. DOI: 10.18500/0869-6632-2009-17-1-3-12

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537.86:530.182, 517.929

Synchronization of periodic oscillation in a delayed-feedback oscillator by external harmonic driving

Ryskin Nikita Mikhailovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Usacheva Svetlana Aleksandrovna, Saratov State University

Dynamics of a delayed-feedback oscillator with cubic nonlinearity driven by an external harmonic signal is considered in a case when in the free-running oscillator periodic regime is realized. Resonance curves, i.e. amplitude–frequency responses of the oscillator are derived analytically. Stability conditions for synchronization regime are analyzed. Synchronization tongues on the driving amplitude – driving frequency parameter plane are presented. General differences from classical picture of synchronization of the systems with one degree of freedom are discussed.

  1. Landa PS. Nonlinear oscillations and waves. Moscow: Fizmatlit; 1997. 496 p. (In Russian).
  2. Dmitriev AS, Kislov VYa. Stochastic oscillations in radiophysics and electronics. Moscow: Nauka; 1989. 277 p. (In Russian).
  3. Kuznetsov SP. Complex dynamics of generators with delayed feedback (review). Izvestiya Vysshikh Uchebnykh Zavedenii. Radiofizika. 1982;25(12):1410–1428.
  4. Pikovsky A, Rosenblum M, Kurts Yu. Synchronization. A fundamental nonlinear phenomenon. Moscow: Tehnosphera; 2003. 493 p. (In Russian).
  5. Rabinovich MI, Trubetskov DI. Introduction to the theory of oscillations and waves. Moscow: Nauka; 1984. 432 p.(In Russian).
  6. Kuznetsov AP, Kuznetsov SP, Ryskin NM. Nonlinear oscillations. Moscow: Nauka; Fizmatlit; 2002. 292 p. (In Russian).
  7. Anishchenko VS, Astakhov VV, Vadivasova TE, Neiman AB, Strelkova GI, Schimansky-Geier L. Nonlinear Effects in Chaotic and Stochastic Systems. Izhevsk-Moscow: Institute of Computer Sciences; 2003. (In Russian).
  8. Ryskin NM, Shigaev AM. Complex dynamics of a simple distributed self-oscillatory model system with delay. Technical Physics. 2002;47(7):795–802. DOI: 10.1134/1.1495037.
  9. Hyrer E, Nersett C, Wanner G. Solution of ordinary differential equations. Non-rigid tasks. Moscow: Mir; 1990. 512 p. (In Russian).
  10. Hookenheimer J, Holmes P. Nonlinear oscillations, dynamical sytems, and ifurcations of vector fileds. Izhevsk-Moscow: RCD; 2002. 559 p. (In Russian).
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