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


For citation:

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: 10.18500/0869-6632-2006-14-5-94-109

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: 173)
Language: 
Russian
Heading: 
Article type: 
Article
UDC: 
517.9

About scaling properties of identical coupled logistic maps with two types of coupling without noise and under influence of external noise

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
Sedova Yuliya Viktorovna, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
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.

Key words: 
Reference: 
  1. Anishchenko VS, Vadivasova TE, Astakhov VV. Nonlinear dynamics of chaotic and stochastic systems. Saratov: Saratov University Publishing; 1999. 367 p. (In Russian).
  2. Mosekilde E, Maistrenko Y, Postnov D. Chaotic synchronization. Applications to living systems. World Scientific Series on Nonlinear Science, Series A. 2002;42. 430 p. DOI: 10.1142/4845.
  3. Kuznetsov SP. Universality and similarity in the behavior of related Feigenbaum systems. Radiophysics and Quantum Electronics. 1985;28(8):991–1007.
  4. Kook H, Ling FH, Schmidt G. Universal behavior of coupled nonlinear systems. Phys Rev A. 1991;43(6):2700–2708. DOI: 10.1103/physreva.43.2700.
  5. Kim SY, Kook H. Period doubling in coupled maps. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1993;48(2):785–799. DOI: 10.1103/physreve.48.785.
  6. Schult RL, Creamer DB, Henyey FS, Wright JA. Symmetric and nonsymmetric coupled logistic maps. Phys Rev A Gen Phys. 1987;35(7):3115–3118. DOI: 10.1103/physreva.35.3115.
  7. Kim SY, Kook H. Critical behavior in coupled nonlinear systems. Phys Rev A. 1992;46(8):R4467—R4470. DOI: 10.1103/physreva.46.r4467.
  8. Reick C, Mosekilde E. Emergence of quasiperiodicity in symmetrically coupled, identical period-doubling systems. Phys. Rev. E. 1995;52(2):1418–1435. DOI: 10.1103/PhysRevE.52.1418.
  9. Rech PC, Beims MW, Gallas JAC. Neimark–Sacker bifurcations in linearly coupled quadratic maps. 2004;1(5). [Electronic recource]. Available from: arXiv:nlin.CD/0408010.
  10. Astakhov VV, Bezruchko BP, Gulyaev YuV, Seleznev YP. Multistable States Of Dissipatively-Connected Feigenbaum System. Pisma v Zhurnal Tekhnicheskoi Fiziki. 1989;15(3):60–65.
  11. Crutchfield JP, Nauenberg M, Rudnik J. Scaling for external noise at the onset of chaos. Phys. Rev. Lett. 1981;46(14):933–935.
  12. Shraiman B, Wayne CE, Martin P.C. Scaling theory for noisy period-doubling transitions to chaos. Phys. Rev. Lett. 1981;46(14):935–939.
  13. 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.
  14. Gulyaev YuV, Kapustina YuV, Kuznetsov AP, Kuznetsov SP. On the scaling properties of two unidirectionally coupled period-doubling systems in the presence of noise. Technical Physics Letters. 2001;27(11):960–963. DOI: 10.1134/1.1424406.
  15. Kuznetsov SP. Dynamical chaos. Moscow: Fizmatlit; 2006. 356 p. (In Russian).
  16. Schuster G. Deterministic chaos. New York: Weinheim. 1988. 240 p.
  17. Fiel D. Scaling for period-doubling sequences with correlated noise. J. Phys. A: Math. Gen. 1987;20:3209–3217. DOI: 10.1088/0305-4470/20/11/024.
  18. Choi S-Y, Lee EK. Scaling behavior at the onset of chaos in the logistic map driven by colored noise. Phys. Lett. A. 1995;205:173–178. DOI: 10.1016/0375-9601(95)00574-M.
Received: 
19.04.2006
Accepted: 
15.07.2006
Published: 
30.11.2006
Short text (in English):
(downloads: 66)