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


Cite this article as:

Ponomarenko V. I., Prokhorov M. D., Seleznev E. P. Estimation of characteristics of self-oscillating time-delay systems in periodic regime. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 6, pp. 86-92. DOI: https://doi.org/10.18500/0869-6632-2007-15-6-86-92

Language: 
Russian

Estimation of characteristics of self-oscillating time-delay systems in periodic regime

Abstract: 

A method is proposed for reconstructing time-delay systems in periodic regime of oscillations. The method is based on the analysis of these systems response to a weak periodic pulse driving. It is shown that proposed method with using of weak driving allows one to recover the delay time of a ring self-oscillating system with time-delayed feedback and to de?ne the order of a model delay-di?erential equation.

Key words: 
DOI: 
10.18500/0869-6632-2007-15-6-86-92
References: 

1. Hale J.K., Lunel S.M.V. Introduction to Functional Differential Equations. New York: Springer, 1993. 2. Bunner M.J., Popp M., Meyer Th., Kittel A., Rau U., Parisi J. Recovery of scalar time-delay systems from time series // Phys. Lett. A. 1996. Vol. 211. P. 345. 3. Voss H., Kurths J. Reconstruction of non-linear time delay models from data by the use of optimal transformations // Phys. Lett. A. 1997. Vol. 234. P. 336. 4. Hegger R., Bunner M.J., Kantz H., Giaquinta A. Identifying and modeling delay feedback systems // Phys. Rev. Lett. 1998. Vol. 81. P. 558. 5. Bezruchko B.P., Karavaev A.S., Ponomarenko V.I., Prokhorov M.D. Reconstruction of time-delay systems from chaotic time series // Phys. Rev. E. 2001. Vol. 64. 056216. 6. Horbelt W., Timmer J., Voss H.U. Parameter estimation in nonlinear delayed feedback systems from noisy data // Phys. Lett. A. 2002. Vol. 299. P. 513. 7. Udaltsov V.S., Larger L., Goedgebuer J.P., Locquet A., Citrin D.S. Time delay identification in chaotic cryptosystems ruled by delay-differential equations // J. of Optical Technology. 2005. Vol. 72. P. 373. 8. Ortin S., Gutierrez J.M., Pesquera L., Vasquez H. Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction // Physica A. 2005. Vol. 351. P. 133. 9. Prokhorov M.D., Ponomarenko V.I., Karavaev A.S., Bezruchko B.P. Reconstruction of time-delayed feedback systems from time series // Physica D. 2005. Vol. 203. P. 209. 10. Рубаник В.П. Колебания квазилинейных систем с запаздыванием. М.: Наука, 1969. 11. Ringwood J.V., Malpas S.C. Slow oscillations in blood pressure via a nonlinear feedback model // Am. J. Physiol. Regulatory Integrative Comp. Physiol. 2001. Vol. 280. P. 1105. 12. Bocharov G.A., Rihan F.A. Numerical modelling in biosciences using delay differential equations // J. Comp. Appl. Math. 2000. Vol. 125. P. 183. 13. Bezruchko B.P., Dikanev T.V., Smirnov D.A. Role of transient processes for reconstruction of model equations from time series // Phys. Rev. E. 2001. Vol. 64. 036210. 14. Харкевич А.А. Борьба с помехами. М.: Наука, 1965. 15. Баскаков С.И. Радиотехнические цепи и сигналы. М.: Высшая школа, 2000. 16. Войшвилло Г.В. Усилительные устройства. М.: Радио и связь,1983.

Short text (in English):
(downloads: 3)
Full text:
(downloads: 36)