For citation:
Kuznetsov A. P., Kapustina J. V. Scaling properties at transition to chaos in model maps in the presence of noise. Izvestiya VUZ. Applied Nonlinear Dynamics, 2000, vol. 8, iss. 6, pp. 78-87. DOI: 10.18500/0869-6632-2000-8-6-78-87
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Article
UDC:
517.9
Scaling properties at transition to chaos in model maps in the presence of noise
Autors:
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Kapustina Julia Viktorovna, Saratov State University
Abstract:
Fundamental scaling properties of bifurcation tree in the absence and in the presence of noise for different maps which show transition to chaos through period—doubling cascade are considered. Numerical method of determination of noise constants for one-dimensional and two-dimensional maps is presented which allows to illustrate scaling properties of bifurcation tree under random noise influence.
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Acknowledgments:
The work was supported by the RFBR (№ 00-02-17509) and CRDF RЕС 006.
Reference:
- Feigenbaum MJ. Quantitative universality for а class of nonlinear transformations. J. Stat. Phys. 1978;19(1):25-52. DOI: 10.1007/BF01020332.
- Peitgen H-O, Jurgens H, Sauge D. Chaos and Fractals. New Frontiers of Science. Nnew Yorrk: Springer; 1992. 999 p. DOI: 10.1007/978-1-4757-4740-9.
- Kuznetsov AP, Kuznetsov SP. Critical dynamics of one-dimensional displays. Part 1. Feigenbaum’s script. Izvestiya VUZ. Applied Nonlinear Dynamics. 1993;1(1):15-33.
- Crutchfield J, Nauenberg M, Rudnick J. Scaling for external noise аt the onset of chaos. Phys. Rev. Lett. 1981;46(14):933-935. DOI: 10.1103/PhysRevLett.46.933.
- Argoul F, Arneodo A, Collet P, Lesne A. Transitions to chaos in the presence of an external periodic field: cross—over effect in the measure of critical exponents. Europhys. Lett. 1987;3(6):643-653. DOI: 10.1209/0295-5075/3/6/001.
- Bezruchko BP, Gulyaev YuV, Kuznetsov SP, Seleznev EP. A new type of critical behaviour of related systems in the transition to chaos. Sov. Phys. Doklady. 1986;287(3):619-622. (in Russian).
- Kuznetsov AP, Kuznetsov SP, Sataev IR. Bicritical dynamics of two—period doublings systems with unidirectional coupling. Int. J. Bifurc. Chaos. 1991;1(4):839-848. DOI: 10.1142/S0218127491000610.
- Kuznetsov AP, Kuznetsov SP, Sataev IR. Variety of types of critical behavior and multistability in period doublings systems with unidirectional coupling near the onset оf chaos. Int. J. Bifurc. Chaos. 1993;3(1):139-152. DOI: 10.1142/S0218127493000106.
- Kuznetsov AP, Kuznetsov SP, Sataev IR. A variety оf 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.
- Sang-Yoon Kim. Bicritical behavior оf period doublings in unidirectionally coupled maps. Phys.Rev. Е. 1999;59(6):6585-6592. DOI: 10.1103/PhysRevE.59.6585.
- Chang SJ, Wortis M, Wright JA. Iterative properties оf а one—dimensional quartic map. Critical lines and tricritical behavior. Phys. Rev. A. 1981;24(5):2669-2684. DOI: 10.1103/PhysRevA.24.2669.
Received:
26.06.2000
Accepted:
20.10.2000
Published:
25.03.2001
Journal issue:
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