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

For citation:

Malyaev V. S., Semenov V. V., Vadivasova T. E. Estimation of the main parameter values of nonlinear dynamic system with noise in experiment. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 3, pp. 17-28. DOI: 10.18500/0869-6632-2012-20-3-17-28

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):
PDF icon 2012no3p017.pdf
(downloads: 143)
Language: 
Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
537.86/.87:530.182
DOI: 
10.18500/0869-6632-2012-20-3-17-28

Estimation of the main parameter values of nonlinear dynamic system with noise in experiment

Autors: 
Malyaev Vladimir Sergeevich, Saratov State University
Semenov V. V., Saratov State University
Vadivasova Tatjana Evgenevna, Saratov State University
Abstract: 

We consider the method of parameter values estimation of dynamical system with noise in application to secure communication. We solve the problem of creating experimental radiophysical generator (Ressler generator) and comparison dynamics of numerical model with radiophysical experiment data. We analyse the influence of noise on the oscillator dynamics and parameter estimation error. We research the possibility of estimation of constant parameter and time-variable parameter, which can be modulated by different form signals. We determine the limits of applicability of the method to experimental generator.

Key words: 
Secure communication
parameter estimation
modulation
nonlinear dynamic system with noise
noise analyzing
Reference: 
  1. Bezruchko BP, Smirnov DA. Mathematical modeling and chaotic time series. Saratov: GOSUNTS «College»; 2005. 320 p. (in Russian).
  2. Pavlov AN, Yanson NB, Anishchenko VS. Reconstruction of Dynamical Systems. Journal of Communications Technology and Electronics. 1999;44(9):999–1014.
  3. Koronovskii AA, Moskalenko OI, Hramov AE. On the use of chaotic synchronization for secure communication. Phys. Usp. 2009;52(12):1213–1238. DOI: 10.3367/UFNe.0179.200912c.1281.
  4. Anishchenko VS, Pavlov AN, Yanson NB. Reconstruction of dynamic systems as applied to secure communications. Technical Physics. 1998;43(12):1401–1407. DOI: 10.1134/1.1259214.
  5. Tikhonov VI, Kharisov VN. Statistical analysis and synthesis of radio engineering devices and systems. Moscow: Radio i Svyaz'; 1991. 608 p. (in Russian).
  6. McSharry PE, Smith LA. Better nonlinear models from noisy data: Attractors with maximum likelihood. Phys. Rev. Lett. 1999;83(21):4285–4288. DOI: 10.1103/PhysRevLett.83.4285.
  7. Timmer J. Parameter estimation in nonlinear stochastic differential equations. Chaos, Solitons & Fractals. 2000;11(15):2571–2578. DOI: 10.1016/S0960-0779(00)00015-1.
  8. Sitz A, Schwarz U, Kurths J, Voss HU. Estimation of parameters and unobserved components for nonlinear systems from noisy time series. Phys. Rev. E. 2002;66:016210. 10.1103/PhysRevE.66.016210.
  9. Smirnov DA, Vlaskin VS, Ponomarenko VI. Estimation of parameters in one-dimensional maps from noisy chaotic time series. Physics Letters A. 2005;336:448–458. DOI: 10.1016/j.physleta.2004.12.092.
  10. Marino IP, Miguez J. On a recursive method for the estimation of unknown parameters of partially observed chaotic systems. Physica D. 2006;220:175–182. DOI: 10.1016/j.physd.2006.07.008.
  11. Marino IP, Zambrano S, Sanjuan VFF, Salvadori F, Meucci R, Arecchi FT. Adaptive procedure for the parameter estimation of a model of a CO2 chaotic laser. International Journal of Bifurcation and Chaos. 2007;17(10):3639–3643. DOI: 10.1142/S0218127407019494.
  12. Marino IP, Miguez J, Meucci R. A Monte Carlo method for adaptively estimating the unknown parameters and the dynamic state of chaotic systems. Phys. Rev. E. 2009;79(5):056218. DOI: 10.1103/PhysRevE.79.056218.
  13. Peng H, Li L, Yang Y, Wang C. Parameter estimation of nonlinear dynamical systems based on integrator theory. Chaos. 2009;19:033130. DOI: 10.1063/1.3216850.
  14. Parlitz U. Estimating model parameters from time series by autosynchronization. Phys. Rev. Lett. 1996;76(8):1232–1235. DOI: 10.1103/PhysRevLett.76.1232.
  15. Parlitz U, Junge L, Kocarev L. Synchronization-based parameter estimation from time series. Phys. Rev. E. 1996;54(6):6253–6259. DOI: 10.1103/physreve.54.6253.
  16. Malyaev VS, Vadivasova TE. Parameter estimation in dynamical systems with additive noise. Nelin. Dinam. 2010;6(2):267–276 (in Russian).
Received: 
12.12.2011
Accepted: 
26.03.2012
Published: 
31.07.2012
Short text (in English):
PDF icon a2012no3p017.pdf
(downloads: 76)
  • 1987 reads