ABOUT SCALING PROPERTIES OF IDENTICAL COUPLED LOGISTIC MAPS WITH TWO TYPES OF COUPLING WITHOUT NOISE AND UNDER INFLUENCE OF EXTERNAL NOISE
Cite this article as:
Kuznetsov A. P., Kuznetsov S. P., Sedova Y. V. ABOUT SCALING PROPERTIES OF IDENTICAL COUPLED LOGISTIC MAPS WITH TWO TYPES OF COUPLING WITHOUT NOISE AND UNDER INFLUENCE OF EXTERNAL NOISE. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 5, pp. 94-109. DOI: https://doi.org/10.18500/0869-6632-2006-14-5-94-109
In this paper the influence of noise in system of identical coupled logistic maps with two types of coupling – dissipative and inertial – is discussed. The corresponding renormalization group analysis is presented. Scaling property in the presence of noise is considered, and necessary illustrations in «numerical experiment style» are given.
1. Анищенко В.С., Вадивасова Т.Е., Астахов В.В. Нелинейная динамика хаотических и стохастических систем // Изд-во Сарат. университета. 1999. 367 с.
2. Mosekilde E., Maistrenko Y., Postnov D. Chaotic synchronization. Applications to living systems // World Scientific Series on Nonlinear Science, Series A. 2002. Vol. 42. 430 p.
3. Кузнецов С.П. Универсальность и подобие в поведении связанных систем Фейгенбаума // Известия вузов. Радиофизика. 1985. Т. 28, No 8. C.991.
4. Kook H, Ling F.H., Schmidt G. Universal behavior of coupled nonlinear systems // Phys. Rev. A. 1991. Vol.43, No 6. P. 2700.
5. Kim S.-Y., Kook H. Period doubling in coupled maps // Phys. Rev. E. 1993. Vol. 48, No 2. P. 785.
6. Schult R.L., Creamer D.B., Henyey F.S., Wright J.A. Symmetric and nonsymmetric coupled logistic maps // Phys. Rev. A. 1987. Vol. 35, No 7. P. 3115.
7. Kim S.-Y., Kook H. Critical behavior in coupled nonlinear systems // Phys. Rev. A. 1992. Vol. 46, No 8. P. 4467.
8. Reick C., Mosekilde E. Emergence of quasiperiodicity in symmetrically coupled, identical period-doubling systems // Phys. Rev. E. 1995. Vol. 52, No 2. P. 1418.
9. Rech P.C., Beims M.W., Gallas J.A.C. Neimark–Sacker bifurcations in linearly coupled quadratic maps // arXiv:nlin.CD/0408010. Vol. 1, No 5. Aug 2004.
10. Астахов В.В., Безручко Б.П., Гуляев Ю.В, Селезнев Е.П. Мультистабильные состояния диссипативно связанных фейгенбаумовских систем // Письма в ЖТФ. 1988. Т. 15, No 3. С. 60.
11. 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.
12. Shraiman B., Wayne C.E., Martin P.C. Scaling theory for noisy period-doubling transitions to chaos // Phys. Rev. Lett. 1981. Vol. 46, No 14. P. 935.
13. 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, No 6. 066207 (12 pages).
14. Гуляев Ю.В., Капустина Ю.В., Кузнецов А.П., Кузнецов С.П. О свойствах скейлинга при воздействии одной системы с удвоениями периода на другую при наличии шума // Письма в ЖТФ. 2001. Т. 27, Вып. 22. С. 58.
15. Кузнецов С.П. Динамический хаос // М.: Физматлит. 2006. 356 с.
16. Шустер Г. Детерминированный хаос // М.: Мир. 1988. 240 с.
17. Fiel D. Scaling for period-doubling sequences with correlated noise // J. Phys. A: Math. Gen. 1987. Vol.20. P.3209-3217.
18. Choi S.-Y., Lee E.K. Scaling behavior at the onset of chaos in the logistic map driven by colored noise // Phys. Lett. A. 1995. Vol. 205. P. 173.
BibTeX
author = {A. P. Kuznetsov and Sergey P. Kuznetsov and Yu. V. Sedova },
title = {ABOUT SCALING PROPERTIES OF IDENTICAL COUPLED LOGISTIC MAPS WITH TWO TYPES OF COUPLING WITHOUT NOISE AND UNDER INFLUENCE OF EXTERNAL NOISE},
year = {2006},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {14},number = {5},
url = {https://old-andjournal.sgu.ru/en/articles/about-scaling-properties-of-identical-coupled-logistic-maps-with-two-types-of-coupling},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2006-14-5-94-109},pages = {94--109},issn = {0869-6632},
keywords = {-},
abstract = {In this paper the influence of noise in system of identical coupled logistic maps with two types of coupling – dissipative and inertial – is discussed. The corresponding renormalization group analysis is presented. Scaling property in the presence of noise is considered, and necessary illustrations in «numerical experiment style» are given. }}