CRITICAL BEHAVIOR OF ASYMMETRICALLY COUPLED NOISY DRIVEN NONIDENTICAL SYSTEMS WITH PERIOD-DOUBLINGS
Cite this article as:
Kuznetsov A. P., Kuznetsov S. P., Savin А. 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: https://doi.org/10.18500/0869-6632-2006-14-5-62-72
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 selfsimilar structure of the parameter plane near the critical point in the model system of two noisy driven coupled logistic maps.
1. Feigenbaum M.J. Quantitative universality for a class of nonlinear transformations // J. of Stat. Phys. 1978. Vol. 19, No 1. P. 25.
2. Feigenbaum M. J. The universal metric properties of nonlinear transformations // J. of Stat. Phys. 1982. Vol. 26, No 6. P. 669.
3. Chang S.J., Wortis M., Wright J.A. Iterative properties of a one-dimensional quartic map. Critical lines and tricritical behavior // Phys. Rev. 1981. Vol. A24. P. 2669.
4. MacKey R.S., Tresser C. Some flesh on skeleton: The bifurcation structure of bimodal maps // Physica. 1987. Vol. D27, No 3. P. 412.
5. Schell M., Fraser S., Kapral R. Subharmonic bifurcations in the sine map: an infinite of bifurcations // Phys. Rev. 1983. Vol. A28, No 1. P. 373.
6. Кузнецов А.П., Кузнецов С.П., Сатаев И.Р. Критическая динамика одномерных отображений. Ч. II. Двухпараметрический переход к хаосу // Изв. вузов. Прикладная нелинейная динамика. 1993. Т. 1, No 3. С. 17.
7. Кузнецов С.П., Сатаев И.Р. Гибрид удвоений периода и касательной бифуркации: количественная универсальность и двухпараметрический скейлинг // Изв. вузов. Прикладная нелинейная динамика. 1995. Т. 3, No 4. С. 3.
8. Feigenbaum M.J., Kadanoff L.P., Shenker S.J. Quasiperiodicity in dissipative systems: A renormalization group analysis // Physica. 1982. Vol. D5. P. 370.
9. Shenker S.J. Scaling behavior in a map of a circle onto itself: Empirical results // Physica. 1982. Vol. D5. P. 126.
10. Rand D. Existence, non-existence and universal breakdown of dissipative golden invariant tori: I. Golden critical circle maps // Nonlinearity. 1992. Vol. 5. P. 639.
11. Kuznetsov S.P. A variety of critical phenomena associated with the golden mean quasiperiodicity // Izvestiya VUZ. Applied Nonlinear Dynamics. 2002. Vol. 10, No 3. P. 22.
12. Shraiman B., Wayne C.E., Martin P.C. Scaling theory for noisy period-doubling transition to chaos // Phys. Rev. Lett. 1981. Vol. 46, No 14. P. 935.
13. 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.
14. Hirsh J.E., Huberman B.A., Scalapino D.J. Theory of intermittency // Phys. Rev. A. 1981. Vol. 25, No 1. C. 519.
15. Hirsh J.E., Nauenberg M., Scalapino D.J. // Phys. Lett. 1982. Vol. 87A. P. 391.
16. Hamm A., Graham R. Scaling for small random perturbations of golden critical circle maps // Phys. Rev. A. 1992. Vol. 46, No 10. P. 6323.
17. Gyorgyi G., Tishby N. Scaling in a stochastic Hamiltonian systems: a renormalization aProach // Phys. Rev. Lett. 1987. Vol. 58, No 6. P. 527.
18. Gyorgyi G., Tishby N. Path integrals in Hamiltonian systems: breakup of the last KAM tori due to random forces // Phys. Rev. Lett. 1989. Vol. 62, No 4. P. 353.
19. Kapustina J.V., Kuznetsov A.P., Kuznetsov S.P., Mosekilde E. Scaling properties of bicritical dynamics in unidirectionally coupled period-doubling systems in the presence of noise // Phys. Rev. E. 2001. Vol. 64, No 6, 006207 (12 pages).
20. 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.
21. Kuznetsov A.P., Kuznetsov S.P., Sedova J.V. Effect of noise on the critical goldenmean quasiperiodic dynamics in the circle map // Physica A, 2006. Vol. 359. P. 48.
22. Kuznetsov S.P. Effect of noise on the dynamics at the torus-doubling terminal point in a quadratic map under quasiperiodic driving // Phys. Rev. E. 2005. Vol. 72, 026205.
23. Kuznetsov S.P., Sataev I.R. Period-doubling for two- dimensional non-invertible maps: Renormalization group analysis and quantitative universality // Physica D. 1997. Vol. 101. P. 249.
24. 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.
25. Kuznetsov S.P., Sataev I.R. New types of critical dynamics for two-dimensional maps // Phys. Lett. A. 1992. Vol. 162, No 3. P. 236.
26. Кузнецов А.П., Савин А.В. Об одном типе перехода порядок-хаос в связанных отображениях с удвоениями периода // Изв. вузов. Прикладная нелинейная динамика. 2003. T. 11, No 6. С. 16.
27. Kuznetsov A.P., Savin A.V., Kim S.Y. On the criticality of the FQ-type in the system of coupled maps with period-doubling // Nonlinear Phenomena in Complex Systems. 2004. Vol. 7, No 1. P. 69.
BibTeX
author = {A. P. Kuznetsov and Sergey P. Kuznetsov and А. V. Savin and I. R. Sataev},
title = {CRITICAL BEHAVIOR OF ASYMMETRICALLY COUPLED NOISY DRIVEN NONIDENTICAL SYSTEMS WITH PERIOD-DOUBLINGS},
year = {2006},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {14},number = {5},
url = {https://old-andjournal.sgu.ru/en/articles/critical-behavior-of-asymmetrically-coupled-noisy-driven-nonidentical-systems-with-period},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2006-14-5-62-72},pages = {62--72},issn = {0869-6632},
keywords = {-},
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 selfsimilar structure of the parameter plane near the critical point in the model system of two noisy driven coupled logistic maps. }}