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


For citation:

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: 10.18500/0869-6632-2006-14-6-31-42

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 194)
Language: 
Russian
Article type: 
Article
UDC: 
517.9

Scaling in dynamics of duffing oscillator under impulses influence with random modulation of parameters

Autors: 
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Sedova Yuliya Viktorovna, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
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.

Key words: 
Reference: 
  1. Kuznetsov SP. Dynamical chaos. Moscow: Fizmatlit; 2006. 356 p. (In Russian).
  2. Crutchfield JP, Nauenberg M, Rudnik J. Scaling for external noise at the onset of chaos. Phys. Rev. Lett. 1981;46(14):933–935. DOI: 10.1103/PHYSREVLETT.46.933.
  3. Hirsch JE, Nauenberg M, Scalapino DJ. Intermittency in the presence of noise: A renormalization group formulation. Phys. Lett. A. 1982;87(8):391–373. DOI: 10.1016/0375-9601(82)90165-7.
  4. Györgyi G, Tishby N. Scaling in stochastic Hamiltonian systems: A renormalization approach. Phys Rev Lett. 1987;58(6):527–530. DOI: 10.1103/PhysRevLett.58.527.
  5. Hamm A, Graham R. Scaling for small random perturbations of golden critical circle maps. Phys Rev A. 1992;46(10):6323–6333. DOI: 10.1103/physreva.46.6323.
  6. Kapustina JV, Kuznetsov AP, Kuznetsov SP, Mosekilde E. Scaling properties of bicritical dynamics in unidirectionally coupled period-doubling systems in the presence of noise. Phys Rev E Stat Nonlin Soft Matter Phys. 2001;64(6):066207. DOI: 10.1103/PhysRevE.64.066207.
  7. Isaeva OB, Kuznetsov SP, Osbaldestin AH. Effect of noise on the dynamics of a complex map at the period-tripling accumulation point. Phys Rev E Stat Nonlin Soft Matter Phys. 2004;69(3):036216. DOI: 10.1103/PhysRevE.69.036216.
  8. Shraiman B, Wayne CE, Martin PC. Scaling theory for noisy period-doubling transitions to chaos, Phys. Rev. Lett. 1981;46(14):935–939. DOI: 10.1103/PHYSREVLETT.46.935.
  9. Kuznetsov AP, Kuznetsov SP, Turukina LV, Mosekilde E. Two-parameter analysis of the scaling behavior at the onset of chaos: Tricritical and pseudo-tricritical points. Physica A. 2001;300(3-4):367–385. DOI: 10.1016/S0378-4371(01)00368-5.
  10. Kuznetsov AP, Turukina LV, Mosekilde E. Dynamical systems of different classes as models of the kicked nonlinear oscillators. Int. J. of Bifurcation and Chaos. 2001;11(4):1065–1077. DOI: 10.1142/S0218127401002547.
  11. Kuznetsov AP, Turukina LV. Dynamical Systems Of Different Classes As Models Of The Kicked Non-Linear Oscillator. Izvestiya VUZ. Applied Nonlinear Dynamics. 2000;8(2):31–42.
  12. Carr Y, Eilbech YC. One-dimensional approximations for a quadratic Ikeda map. Phys. Lett. A. 1984;104(2):59–62. DOI: 10.1016/0375-9601(84)90962-9.
  13. Kuznetsov AP, Kapustina JV. Scaling properties at transition to chaos in model maps in the presence of noise. Izvestiya VUZ. Applied Nonlinear Dynamics. 2000;8(6):78–87.
  14. Marcus M, Hess B. Lyapunov exponents of the logistic map with periodic forcing. Computers & Graphics. 1989;13(4):553–558.
  15. Rossler J, Kiwi M, Hess B, Marcus M. Modulated nonlinear processes and a novel mechanism to induce chaos. Phys. Rev. A. 1989;39(11):5954–5960. DOI: 10.1103/physreva.39.5954.
  16. Marcus M. Chaos in maps with continuous and discontinuous maxima. Computers in physics. 1990;4(5):481–493. DOI: 10.1063/1.4822940.
  17. Bastos de Figueireido JC, Malta CP. Lyapunov graph for two-parameter map: Application to the circle map. Int. J. of Bifurcation and Chaos. 1998;8(2):281–293. DOI: 10.1142/S0218127498000176.
  18. Kuznetsov AP, Kuznetsov SP, Sataev IR. A variety of period-doubling universality classes in multi-parameter analysis of transition to chaos. Physica D. 1997;109(1-2):91–112.
  19. Kuznetsov AP, Kuznetsov SP, Sataev IR. Three-parameter scaling for one-dimensional maps. Phys. Lett. A. 1994;189(5):367–373. DOI: 10.1016/0375-9601(94)90018-3.
Received: 
03.05.2006
Accepted: 
27.06.2006
Published: 
29.12.2006
Short text (in English):
(downloads: 66)