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

For citation:

Prokhorov M. D., Ponomarenko V. I., Khorev V. S. Delay time estimation from time series based on nearest neighbor method. Izvestiya VUZ. Applied Nonlinear Dynamics, 2014, vol. 22, iss. 1, pp. 3-15. DOI: 10.18500/0869-6632-2014-22-1-3-15

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 prokhorov_ver_6.pdf
(downloads: 197)
Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
537.86
DOI: 
10.18500/0869-6632-2014-22-1-3-15

Delay time estimation from time series based on nearest neighbor method

Autors: 
Prokhorov Mihail Dmitrievich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Ponomarenko Vladimir Ivanovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Khorev Vladimir Sergeevich, Innopolis University
Abstract: 

The method is proposed for delay time estimation in time-delay systems from their time series. The method is based on the nearest neighbor method. It can be applied to a wide class of time-delay systems and it is still efficient under very high levels of dynamical and measurement noise.

Key words: 
Time-delay systems
time series analysis
parameter estimation
Reference: 
  1. Ikeda K. Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system. Opt. Commun. 1979;30(2):257—261. DOI: 10.1016/0030-4018(79)90090-7.
  2. Lang R, Kobayashi K. External optical feedback effects on semiconductor injection lasers. IEEE Journal of Quantum Electronics. 1980;16(3):347-355. DOI: 10.1109/JQE.1980.1070479.
  3. Erneux T. Applied Delay Differential Equations. New York: Springer; 2009. DOI:10.1007/978-0-387-74372-1.
  4. Epstein IR. Delay effects and differential delay equations in chemical-kinetics. Int. Rev. in Phys. Chem. 1992;11:135—160. DOI: 10.1080/01442359209353268.
  5. Mokhov II, Smirnov DA. El Nino Southern Oscillation drives North Atlantic Oscillation as revealed with nonlinear techniques from climatic indices. Geophys. Research Lett. 2006;33:L03708. DOI: 10.1029/2005GL024557.
  6. Mackey MC, Glass L. Oscillations and chaos in physiological control systems. Science. 1977;197(4300):287—289. DOI: 10.1126/science.267326.
  7. Kuang Y. Delay Differential Equations with Applications in Population Dynamics. Boston: Academic Press; 1993.
  8. Bocharov GA, Rihan FA. Numerical modelling in biosciences using delay differential equations. Journal Comp. Appl. Math. 2000;125:183—199. DOI: 10.1016/S0377-0427(00)00468-4.
  9. Fowler AC, Kember G. Delay recognition in chaotic time series. Phys. Lett. A. 1993;175:402—408.
  10. Hegger R, Bunner MJ, Kantz H, Giaquinta A. Identifying and modeling delay feedback systems. Phys. Rev. Lett. 1998;81(3):558—561. DOI:10.1103/PHYSREVLETT.81.558.
  11. Bünner MJ, Ciofini M, Giaquinta A, Hegger R, Kantz H, Meucci R, Politi A. Reconstruction of systems with delayed feedback: (I) Theory. Eur. Phys. J. D. 2000;10(2):165—176. DOI:10.1007/s100530050538.
  12. Tian YC, Gao F. Extraction of delay information from chaotic time series based on information entropy. Physica D. 1997;108:113—118.
  13. Kaplan DT, Glass L. Coarse-grained embeddings of time series: Random walks, gaussian random process, and deterministic chaos. Physica D. 1993;64:431—454. DOI:10.1016/0167-2789(93)90054-5.
  14. Bunner MJ, Meyer Th, Kittel A, Parisi J. Recovery of the time-evolution equation of time-delay systems from time series. Phys. Rev. E. 1997;56:5083—5089. DOI:10.1103/PhysRevE.56.5083
  15. Voss H, Kurths J. Reconstruction of non-linear time delay models from data by the use of optimal transformations. Phys. Lett. A. 1997;234:336—344. DOI:10.1016/S0375-9601(97)00598-7.
  16. Ellner SP, Kendall BE, Wood SN, McCauley E, Briggs CJ. Inferring mechanism from time-series data: Delay differential equations. Physica D. 1997;110(3-4):182—194. DOI: 10.1016/S0167-2789(97)00123-1.
  17. Ponomarenko VI, Prokhorov MD, Karavaev AS, Bezruchko BP. Recovery of parameters of delayed-feedback systems from chaotic time series. Journal of Experimental and Theoretical Physics. 2005;100(3):457—467. DOI: 10.1134/1.1901758.
  18. Udaltsov VS, Larger L, Goedgebuer JP, Locquet A, Citrin DS. Time delay identification in chaotic cryptosystems ruled by delay-differential equations. J. Opt. Technology. 2005;72(5):373—377. DOI: 10.1364/JOT.72.000373.
  19. Zunino L, Soriano MC, Fischer I, Rosso OA, Mirasso CR. Permutation-information-theory approach to unveil delay dynamics from time-series analysis. Phys. Rev. E. 2010;82(4):046212. DOI: 10.1103/PhysRevE.82.046212.
  20. Horbelt W, Timmer J, Voss HU. Parameter estimation in nonlinear delayed feed-back systems from noisy data. Phys. Lett. A. 2002;299(5-6):513—521. DOI: 10.1016/S0375-9601(02)00748-X.
  21. Dai C, Chen W, Li L, Zhu Y, Yang Y. Seeker optimization algorithm for parameter estimation of time-delay chaotic systems. Phys. Rev. E. 2011;83(3):036203. DOI:10.1103/PhysRevE.83.036203.
  22. Sorrentino F. Identification of delays and discontinuity points of unknown systems by using synchronization of chaos. Phys. Rev. E. 2010;81(6):066218. DOI: 10.1103/PhysRevE.81.066218.
  23. Ma H, Xu B, Lin W, Feng J. Adaptive identification of time delays in nonlinear dynamical models. Phys. Rev. E. 2010;82(6):066210. DOI: 10.1103/PhysRevE.82.066210.
  24. Siefert M. Practical criterion for delay estimation using random perturbations. Phys. Rev. E. 2007;76(2):026215. DOI: 10.1103/PhysRevE.76.026215.
  25. Ponomarenko VI, Prokhorov MD. Recovery of systems with a linear filter and nonlinear delay feedback in periodic regimes. Phys. Rev. E. 2008;78(6):066207. DOI: 10.1103/PhysRevE.78.066207.
  26. Yu D, Frasca M, Liu F. Control-based method to identify underlying delays of a nonlinear dynamical system. Phys. Rev. E. 2008;78(4):046209. DOI: 10.1103/PhysRevE.78.046209.
  27. Prokhorov MD, Ponomarenko VI. Reconstruction of time-delay systems using small impulsive disturbances. Phys. Rev. E. 2009;80(6):066206. DOI: 10.1103/PhysRevE.80.066206.
  28. Farmer JD, Sidorowich JJ. Predicting chaotic time series. Phys. Rev. Lett. 1987;59(8):845—848. DOI: 10.1103/PhysRevLett.59.84.
  29. García P, Jiménez J, Marcano A, Moleiro F. Local optimal metrics and nonlinear modeling of chaotic time series. Phys. Rev. Lett. 1996;76(9):1449—1452. DOI: 10.1103/PhysRevLett.76.1449.
  30. Villermaux E. Memory-induced low frequency oscillations in closed convection boxes. Phys. Rev. Lett. 1995;75(25):4618—4621. DOI: 10.1103/PhysRevLett.75.4618
Received: 
25.06.2013
Accepted: 
06.12.2013
Published: 
30.04.2014
Short text (in English):
PDF icon a2014no1p003_1.pdf
(downloads: 103)
  • 2192 reads