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

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Kuznetsov A. P., Kuznetsov S. P., Savin A. V., Sataev I. R. Critical behavior of asymmetrically coupled noisy driven nonidentical systems with period-doublings. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 5, pp. 62-72. DOI: 10.18500/0869-6632-2006-14-5-62-72

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Language: 
Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2006-14-5-62-72

Critical behavior of asymmetrically coupled noisy driven nonidentical systems with period-doublings

Autors: 
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Savin Aleksej Vladimirovich, Saratov State University
Sataev Igor Rustamovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

We investigated the influence of external noise on the critical behavior typical to nonidentical coupled systems with period-doubling. We obtained the numerical value of the scaling factor for noise amplitude by means of the renormalization group analysis. Also we demonstrated the self-similar structure of the parameter plane near the critical point in the model system of two noisy driven coupled logistic maps.

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Reference: 
  1. Feigenbaum MJ. Quantitative universality for a class of nonlinear transformations. J. of Stat. Phys. 1978;19(1):25–52. DOI: 10.1007/BF01020332.
  2. Feigenbaum MJ. The universal metric properties of nonlinear transformations. J. of Stat. Phys. 1982;26(6):669–706. DOI: 10.1007/BF01107909.
  3. Chang SJ, Wortis M, Wright JA. Iterative properties of a one-dimensional quartic map. Critical lines and tricritical behavior. Phys. Rev. 1981;A24:2669.
  4. MacKey RS, Tresser C. Some flesh on skeleton: The bifurcation structure of bimodal maps. Physica. 1987;D27(3):412–422. DOI: 10.1016/0167-2789(87)90040-6.
  5. Schell M, Fraser S, Kapral R. Subharmonic bifurcations in the sine map: an infinite of bifurcations. Phys. Rev. 1983;A28(1):373–378. DOI: 10.1103/PHYSREVA.28.373.
  6. Kuznetsov AP, Kuznetsov SP, Sataev IR. Critical dynamics of one-dimensional mappings. C.II. Two-parameter transition to chaos. Izvestiya VUZ. Applied Nonlinear Dynamics. 1993;1(3):17–35.
  7. Kuznetsov SP, Sataev IR. Hybrid of doubles of period and tangent bifurcation: quantitative versatility and two-parameter skaling. Izvestiya VUZ. Applied Nonlinear Dynamics. 1995;3(4):3.
  8. Feigenbaum MJ, Kadanoff LP, Shenker SJ. Quasiperiodicity in dissipative systems: A renormalization group analysis. Physica. 1982;5:370–386. DOI: 10.1016/0167-2789(82)90030-6.
  9. Shenker SJ. Scaling behavior in a map of a circle onto itself: Empirical results. Physica. 1982;5(2-3):405–411. DOI: 10.1016/0167-2789(82)90033-1.
  10. Rand D. Existence, non-existence and universal breakdown of dissipative golden invariant tori: I. Golden critical circle maps. Nonlinearity. 1992;5(3):639–662.
  11. Kuznetsov SP. A variety of critical phenomena associated with the golden mean quasiperiodicity. Izvestiya VUZ. Applied Nonlinear Dynamics. 2002;10(3):22–39.
  12. Shraiman B, Wayne CE, Martin PC. Scaling theory for noisy period-doubling transition to chaos. Phys. Rev. Lett. 1981;46(14):935–939. DOI: 10.1103/physrevlett.46.935.
  13. Crutchfield JP, Nauenberg M, Rudnik J. Scaling for external noise at the onset of chaos. Phys. Rev. Lett. 1981;46(14):933–935.
  14. Hirsh JE, Huberman BA, Scalapino DJ. Theory of intermittency. Phys. Rev. A. 1981;25(1):519–532. DOI: 10.1103/PHYSREVA.25.519.
  15. Hirsh JE, Nauenberg M, Scalapino DJ. Intermittency in the presence of noise: A renormalization group formulation. Phys. Lett. 1982;87A:391–393. DOI: 10.1016/0375-9601(82)90165-7.
  16. 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.
  17. 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.
  18. Györgyi G, Tishby N. Path integrals in Hamiltonian systems: Breakup of the last Kolmogorov-Arnold-Moser torus due to random forces. Phys Rev Lett. 1989;62(4):353–356. DOI: 10.1103/PhysRevLett.62.353.
  19. 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.
  20. 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.
  21. Kuznetsov AP, Kuznetsov SP, Sedova JV. Effect of noise on the critical goldenmean quasiperiodic dynamics in the circle map. Physica A. 2006;359:48–64. DOI: 10.1016/J.PHYSA.2005.05.002.
  22. Kuznetsov SP. Effect of noise on the dynamics at the torus-doubling terminal point in a quadratic map under quasiperiodic driving. Phys. Rev. E. 2005;72(2):026205. DOI: 10.1103/PHYSREVE.72.026205.
  23. Kuznetsov SP, Sataev IR. Period-doubling for two- dimensional non-invertible maps: Renormalization group analysis and quantitative universality. Physica D. 1997;101(3-4):249–269. DOI: 10.1016/S0167-2789(96)00237-0.
  24. 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. DOI: 10.1016/S0167-2789(97)00162-0.
  25. Kuznetsov SP, Sataev IR. New types of critical dynamics for two-dimensional maps. Phys. Lett. A. 1992;162(3):236–242. DOI: 10.1016/0375-9601(92)90440-w.
  26. Kuznetsov AP, Savin AV. On some type of transition from order to chaos in the system of coupled maps with period doubling. Izvestiya VUZ. Applied Nonlinear Dynamics. 2003;11(6):16–31.
  27. Kuznetsov AP, Savin AV, Kim SY. On the criticality of the FQ-type in the system of coupled maps with period-doubling. Nonlinear Phenomena in Complex Systems. 2004;7(1):69–77.
Received: 
03.02.2006
Accepted: 
26.04.2006
Published: 
30.11.2006
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