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

Cite this article as:

Kuznecov 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:


Features of the parameter plane of two nonidentical coupled van der pol – duffing oscillators

Kuznecov Aleksandr Petrovich, Saratov State University
Paksjutov Vladimir Igorevich, Saratov State University

The system of two nonidentical dissipative coupled Van der Pol – Du?ng 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 di?erential model and the in?uence of the phase nonlinearity on its con?guration are discussed. The case of the nonsymmetrical nonlinearity in oscillators is also considered.

Key words: 

1. Пиковский А., Розенблюм М., Куртц Ю. Синхронизация. Фундаментальное нелинейное явление. М.: Техносфера, 2003. 496 с. 2. Aronson D.G., Ermentrout G.B., Kopell N. Amplitude Response of Coupled Oscillators // Physica D. 1990. Vol. 41. P. 403. 3. Кузнецов С.П. Динамический хаос. Сер. Современная теория колебаний и волн. М.: Изд-во Физматлит, 2001. 296 с. 4. Кузнецов А.П., Паксютов В.И. О динамике двух связанных осцилляторов Ван дер Поля – Дуффинга с диссипативной связью // Изв. вузов. Прикладная нелинейная динамика. 2003. Т. 11, No 6. 5. Storti D.W., Rand R.H. Dynamics of two strongly coupled Van der Pol oscillators // Int. J. Non-Linear Mechanics. 1982. Vol. 17, No 3, 143-152. 6. 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. Non-Linear Mechanics. 1988. Vol. 23, No 5/6, 369-376. 7. Poliashenko M., McKay S.R., Smith C.W. Chaos and nonisochronism in weakly coupled nonlinear oscillators // Phys. Rev. A. 1991. Vol. 44. P. 3452. 8. Poliashenko M., McKay S.R., Smith C.W. Hysteresis of synchronous –  asynchronous regimes in a system of two coupled oscillators // Phys. Rev. A. 1991. Vol. 43. P. 5638. 9. Pastor I., Perez-Garcia V.M., Encinas-Sanz F., Guerra J.M. Ordered and chaotic behavior of two coupled van der Pol oscillators // Phys. Rev. E. 1993. Vol. 48. P.171. 10. Camacho E., Rand R.H., Howland H. Dynamics of two van der Pol oscillators coupled via a bath // Int. J. of Solids and Structures. 2004. Vol. 41. P. 2133-2143.

Short text (in English): 
Full text: