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

For citation:

Emelianova Y. P., Kuznetsov A. P. Coupled self-­sustained oscillators of different nature by example of van der Pol system and brusselator. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 5, pp. 54-66. DOI: 10.18500/0869-6632-2010-18-5-54-66

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: 100)
Article type: 

Coupled self-­sustained oscillators of different nature by example of van der Pol system and brusselator

Emelianova Yulija Pavlovna, Saratov State University
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

Problem of interaction between self­sustained oscillating systems of different nature is discussed by an example of coupled brusselator and van der Pol oscillator. Picture of leading oscillator changing with the growth of coupling parameter is shown. Areas of different types of dynamics are indicated in the parameter space. The case of essentially different eigenfrequencies is discussed.

  1. Pikovsky A, Rosenblum M, Kurts Yu. Synchronization: A fundamental nonlinear phenomenon. Moscow: Tehnosphera; 2003. 493 p.
  2. Landa PS. Nonlinear Oscillations and Waves. Moscow: Nauka; 1997. 495 p. (in Russian).
  3. Landa PS. Self-Oscillation in Systems with Finite Number of Degress of Freedom. Moscow: Nauka; 1980. 360 p. (in Russian).
  4. Blekhman II. Synchronization in nature and technology. Moscow: Nauka; 1981. 351 p. (in Russian).
  5. 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.
  6. Rand R, Holmes PJ. Bifurcation of periodic motions in two weakly coupled van der Pol oscillators. Int. J. Non-Linear Mechanics. 1980;15:387–399. DOI: 10.1016/0020-7462(80)90024-4.
  7. 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.
  8. 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.
  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. DOI: 10.1103/physreve.48.171.
  10. Kuznetsov AP, Paksyutov VI. On the dynamics of two van der Pol – Duffing oscillators with dissipative coupling. Izvestiya VUZ. Applied Nonlinear Dynamics. 2003;11(6):48–64 (in Russian).
  11. Ivanchenko MV, Osipov GV, Shalfeev VD, Kurths J. Synchronization of two nonscalar-coupled limit-cycle oscillators. Physica D. 2004;189(1–2):8–30. DOI: 10.1016/j.physd.2003.09.035.
  12. Kuznetsov AP, Paksjutov VI, Roman JP. Features of the synchronization of coupled van der Pol oscillators with nonidentical control parameters. Technical Physics Letters. 2007;33:636–638. DOI: 10.1134/S1063785007080032.
  13. Kuznetsov AP, Paksjutov VI, Roman JP. Properties of synchronization in the system of nonidentical coupled van der pol and van der Pol – Duffing oscillators. Broadband synchronization. Izvestiya VUZ. Applied Nonlinear Dynamics. 2007;15(4):3–15 (in Russian). DOI: 10.18500/0869-6632-2007-15-4-3-15.
  14. Kuznetsov AP, Roman JuP. Properties of synchronization in the systems of nonidentical coupled van der Pol and van der Pol–Duffing oscillators. Broadband synchronization. Physica D. 2009;238(16):1499–1506. DOI: 10.1016/j.physd.2009.04.016.
  15. Astakhov VV, Koblyansky SA, Vadivasova TE, Anishchenko VS. Bifurcation analysis of two dissipatively coupled van der Pol oscillators. Telecommunications and Radio Engineering. 2008;9:61–68 (in Russian).
  16. Astakhov VV, Kobljanskij SA, Shabunin AV. Bifurcation analysis of synchronization and amplitude death in coupled generators with inertial nonlinearity. Izvestiya VUZ. Applied Nonlinear Dynamics. 2010;18(2):79–97 (in Russian). DOI: 10.18500/0869-6632-2010-18-2-79-97.
  17. Kuznetsov A. P., Roman J. P., Seleznev E. P. Synchronization in coupled self­sustained oscillators with non­-identical parameters. Izvestiya VUZ. Applied Nonlinear Dynamics. 2010;18(2):62–78 (in Russian). DOI: 10.18500/0869-6632-2010-18-2-62-78.
  18. Kuznetsov AP, Kuznetsov SP, Ryskin NM. Nonlinear oscillations. Series: Modern theory of oscillations and waves. 2nd ed. Moscow: Fizmatlit; 2006. 292 p. (in Russian).
  19. Kuznetsov SP. Dynamical chaos. Series: Modern theory of oscillations and waves. 2nd ed. reprint. and additional Moscow: Fizmatlit; 2006. 356 p. (in Russian).
  20. Ivanchenko MV. Generation and synchronization of oscillations in systems with «multiscale» chaos. N. Novgorod: Nizhny Novgorod University Publ.; 2007. 138 p. (in Russian).
Short text (in English):
(downloads: 56)