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

For citation:

Kuznetsov A. P., Paksjutov V. I. Features of the parameter plane of two nonidentical coupled Van der Pol – Duffing oscillators. Izvestiya VUZ. Applied Nonlinear Dynamics, 2005, vol. 13, iss. 4, pp. 3-19. DOI: 10.18500/0869-6632-2005-13-4-3-19

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text:
(downloads: 81)
Article type: 

Features of the parameter plane of two nonidentical coupled Van der Pol – Duffing oscillators

Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Paksjutov Vladimir Igorevich, Saratov State University

The system of two nonidentical dissipative coupled Van der Pol – Duffing oscillators is considered. A possibility of Adler equation application to describe the synchronization areas is shown due to transition to the closed equations. There is a nontrivial form of the main synchronization tongue on the plane of the control parameters. The view of synchronization tongues system of the original differential model and the influence of the phase nonlinearity on its configuration are discussed. The case of the nonsymmetrical nonlinearity in oscillators is also considered.

Key words: 
  1. Pikovsky A, Rosenblum M, Kurths J. Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge, UK: Cambridge University Press; 2001. 411 p. DOI: 10.1017/CBO9780511755743.
  2. Aronson DG, Ermentrout GB, Kopell N. Amplitude response of coupled oscillators. Physica D. 1990;41(3):403–449. DOI: 10.1016/0167-2789(90)90007-C.
  3. Kuznetsov SP. Dynamic Chaos. Modern Theory of Vibrations and Waves. Moscow: Fizmatlit; 2001. 296 p. (in Russian).
  4. Kuznetsov AP, Paksyutov VI. On the dynamics of two coupled van der Pol - Duffing oscillators with dissipative coupling. Izvestiya VUZ. Applied Nonlinear Dynamics. 2003;11(6):48–64 (in Russian).
  5. Storti DW, Rand RH. Dynamics of two strongly coupled Van der Pol oscillators. Int. J. Non-Linear Mechanics. 1982;17(3):143–152. DOI: 10.1016/0020-7462(82)90014-2.
  6. Chakraborty T, Rand RH. The transition from phase locking to drift in a system of two weakly coupled van der Pol oscillators. Int. J. Non-Linear Mechanics. 1988;23(5–6):369–376. DOI: 10.1016/0020-7462(88)90034-0.
  7. Poliashenko M, McKay SR, Smith CW. Chaos and nonisochronism in weakly coupled nonlinear oscillators. Phys. Rev. A. 1991;44(6):3452–3456. DOI: 10.1103/physreva.44.3452.
  8. Poliashenko M, McKay SR, Smith CW. Hysteresis of synchronous –  asynchronous regimes in a system of two coupled oscillators. Phys. Rev. A. 1991;43(10):5638–5641. DOI: 10.1103/physreva.43.5638.
  9. Pastor I, Perez-Garcia VM, Encinas-Sanz F, Guerra JM. Ordered and chaotic behavior of two coupled van der Pol oscillators. Phys. Rev. E. 1993;48(1):171–182. DOI: 10.1103/physreve.48.171.
  10. Camacho E, Rand RH, Howland H. Dynamics of two van der Pol oscillators coupled via a bath. Int. J. Solids Structures. 2004;41(8):2133–2143. DOI: 10.1016/j.ijsolstr.2003.11.035.
Short text (in English):
(downloads: 51)