SCALING IN DYNAMICS OF DUFFING OSCILLATOR UNDER IMPULSES INFLUENCE WITH RANDOM MODULATION OF PARAMETERS


Cite this article as:

Kuznetsov A. P., Sedova Y. V. SCALING IN DYNAMICS OF DUFFING OSCILLATOR UNDER IMPULSES INFLUENCE WITH RANDOM MODULATION OF PARAMETERS. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 6, pp. 31-42. DOI: https://doi.org/10.18500/0869-6632-2006-14-6-31-42


In the work nonlinear Duffing oscillator is considered under impulse excitation with two ways of introduction of the random additive term simulating noise, - with help of amplitude modulation and modulation of period of impulses sequence. The scaling properties both in the Feigenbaum scenario and in the tricritical case are shown.

Key words: 
-
DOI: 
10.18500/0869-6632-2006-14-6-31-42
Literature

1. Кузнецов С.П. Динамический хаос (курс лекций). 2-е изд., испр. и доп. М.: Физматлит. 2006. 356 с.

2. Crutchfield J.P., Nauenberg M., Rudnik J. Scaling for external noise at the onset of chaos // Phys. Rev. Lett. 1981. Vol. 46, No 14. P. 933.

3. Hirsch J.E., Nauenberg M., Scalapino D.J. Intermittency in the presence of noise: A renormalization group formulation // Phys. Lett. A. 1982. Vol. 87. P. 391.

4. Gyorgyi G., Tishby N.  ̈ Scaling in stochastic Hamiltonian systems: A renormalization approach // Phys. Rev. Lett. 1987. Vol. 58, No 6. P. 527.

5. Hamm A., Graham R. Scaling for small random perturbations of golden critical circle maps // Phys. Rev. A. 1992. Vol. 46, No 10. P. 6323.

6. Kapustina J.V., Kuznetsov A.P., Kuznetsov S.P., Mosekilde E. Scaling properties of bicritical dynamics in unidirectionally coupled period-doubling systems in presence of noise // Phys. Rev. E. 2001. Vol. 64, 066207.

7. Isaeva O.B., Kuznetsov S.P., Osbaldestin A.H. Effect of noise on the dynamics of a complex map at the period-tripling accumulation point // Phys. Rev. E. 2004. Vol. 69, 036216.

8. Shraiman B., Wayne C.E., Martin P.C. Scaling theory for noisy period-doubling transitions to chaos // Phys. Rev. Lett. 1981. Vol. 46, No14. P. 935.

9. Kuznetsov A.P., Kuznetsov S.P., Turukina L.V., Mosekilde E. Two-parameter analysis of the scaling behavior at the onset of chaos: Tricritical and pseudo-tricritical points // Physica A. 2001. Vol. 300, No 3-4. P. 367.

10. Kuznetsov A.P., Turukina L.V., Mosekilde E. Dynamical systems of different classes as models of the kicked nonlinear oscillators // Int. J. of Bifurcation and Chaos. 2001. Vol. 11, No4. P. 1065.

11. Кузнецов А.П., Тюрюкина Л.В. Динамические системы разных классов как модели нелинейного осциллятора с импульсным воздействием // Известия вузов. Прикладная нелинейная динамика. 2000. Том 8, No 2. C. 31-42.

12. Carr Y., Eilbech Y.C. One-dimensional approximations for a quadratic Ikeda map // Phys. Lett. A. 1984. Vol. 104. P. 59.

13. Кузнецов А.П., Капустина Ю.В. Свойства скейлинга при переходе к хаосу в модельных отображениях с шумом // Известия вузов. Прикладная нелинейная динамика. 2000. Том 8, No 6. C. 78.

14. Marcus M., Hess B. Lyapunov exponents of the logistic map with periodic forcing // Computers & Graphics. 1989. Vol. 13, No 4. P. 553.

15. Rossler J., Kiwi M., Hess B., Marcus M.  ̈ Modulated nonlinear processes and a novel mechanism to induce chaos // Phys. Rev. A. 1989. Vol. 39, No 11. P. 5954.

16. Marcus M. Chaos in maps with continuous and discontinuous maxima // Computers in physics. 1990. September/October. P. 481.

17. Bastos de Figueireido J.C., Malta C.P. Lyapunov graph for two-parameter map: Application to the circle map // Int. J. of Bifurcation and Chaos. 1998. Vol. 8, No 2. P. 281.

18. Kuznetsov A.P., Kuznetsov S.P., Sataev I.R. A variety of period-doubling universality classes in multi-parameter analysis of transition to chaos // Physica D. 1997. Vol. 109. P. 91.

19. Kuznetsov A.P., Kuznetsov S.P., Sataev I.R. Three-parameter scaling for one-dimensional maps // Phys. Lett. A. 1994. Vol. 189. P. 367.

Status: 
одобрено к публикации
Short Text (PDF): 
Full Text (PDF): 

BibTeX

@article{Кузнецов-IzvVUZ_AND-14-6-31,
author = {A. P. Kuznetsov and Yu. V. Sedova },
title = {SCALING IN DYNAMICS OF DUFFING OSCILLATOR UNDER IMPULSES INFLUENCE WITH RANDOM MODULATION OF PARAMETERS},
year = {2006},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {14},number = {6},
url = {https://old-andjournal.sgu.ru/en/articles/scaling-in-dynamics-of-duffing-oscillator-under-impulses-influence-with-random-modulation},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2006-14-6-31-42},pages = {31--42},issn = {0869-6632},
keywords = {-},
abstract = {In the work nonlinear Duffing oscillator is considered under impulse excitation with two ways of introduction of the random additive term simulating noise, - with help of amplitude modulation and modulation of period of impulses sequence. The scaling properties both in the Feigenbaum scenario and in the tricritical case are shown. }}