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

For citation:

Karavaev A. S., Ponomarenko V. I., Prokhorov M. D. Reconstruction of neutral time-delay systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 5, pp. 3-16. DOI: 10.18500/0869-6632-2011-19-5-3-16

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: 139)
Article type: 

Reconstruction of neutral time-delay systems

Karavaev Anatolij Sergeevich, Saratov State University
Ponomarenko Vladimir Ivanovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Prokhorov Mihail Dmitrievich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

The methods are proposed for the reconstruction of time-delay systems modeled by neutral delay-differential equations from their time series. The methods are successfully applied to the recovery of generalized Mackey–Glass equation and equations modeling ship rolling and human movement from simulated data.

  1. Mackey MC, Glass L. Oscillations and chaos in physiological control systems. Science. 1977;197(4300):287–289. DOI: 10.1126/science.267326.
  2. 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.
  3. Epstein IR. Delay effects and differential delay equations in chemical-kinetics. Int. Rev. Phys. Chem. 1992;11(1):135–160. DOI: 10.1080/01442359209353268.
  4. Kuang Y. Delay Differential Equations with Applications in Population Dynamics. Boston: Academic Press; 1993. 412 p.
  5. Voss H, Kurths J. Reconstruction of non-linear time delay models from data by the use of optimal transformations. Phys. Lett. A. 1997;234(5):336–344. DOI: 10.1016/S0375-9601(97)00598-7.
  6. Tian YC, Gao F. Extraction of delay information from chaotic time series based on information entropy. Physica D. 1997;108(1–2):113–118. DOI: 10.1016/S0167-2789%2897%2982008-8.
  7. 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.
  8. Bunner 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.
  9. 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.
  10. Ortin S, Gutierrez JM, Pesquera L, Vasquez H. Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction. Physica A. 2005;351(1):133–141. DOI: 10.1016/j.physa.2004.12.015.
  11. Siefert M. Practical criterion for delay estimation using random perturbations. Phys. Rev. E. 2007;76(2):026215. DOI: 10.1103/physreve.76.026215.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Gopalsamy K. Oscillations in neutral delay-differential equations. J. Math. Phys. Sci. 1987;21:23.
  17. Gopalsamy K. Stability and Oscillations in Delay Differential Equations of Population Dynamics. Dordrecht: Kluwer; 1992. 502 p. DOI: 10.1007/978-94-015-7920-9.
  18. Hale JK, Lunel SMV. Introduction to Functional Differential Equations. New York: Springer; 1993. 450 p. DOI: 10.1007/978-1-4612-4342-7.
  19. Bocharov GA, Rihan FA. Numerical modelling in biosciences using delay differential equations. J. Comp. Appl. Math. 2000;125(1–2):183–199. DOI: 10.1016/S0377-0427(00)00468-4.
  20. Patanarapeelert K, Frank TD, Friedrich R, Beek PJ, Tang IM. A data analysis method for identifying deterministic components of stable and unstable time-delayed systems with colored noise. Phys. Lett. A. 2006;360(1):190–198. DOI: 10.1016/j.physleta.2006.08.003.
  21. Peterka RJ. Sensorimotor integration in human postural control. J. Neurophysiol. 2002;88(3):1097–1118. DOI: 10.1152/jn.2002.88.3.1097.  
Short text (in English):
(downloads: 88)