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


For citation:

Mohammad Y. H., Pavlov A. N. Largest Lyapunov exponent of chaotic oscillatory regimes computing from point processes in the noise presence. Izvestiya VUZ. Applied Nonlinear Dynamics, 2015, vol. 23, iss. 6, pp. 31-39. DOI: 10.18500/0869-6632-2015-23-6-31-39

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: 156)
Language: 
Russian
Article type: 
Article
UDC: 
51-73

Largest Lyapunov exponent of chaotic oscillatory regimes computing from point processes in the noise presence

Autors: 
Mohammad Yasir Halaf, Saratov State University
Pavlov Aleksej Nikolaevich, Saratov State University
Abstract: 

We propose a modified method for computing of the largest Lyapunov exponent of chaotic oscillatory regimes from point processes at the presence of measurement noise that does not influence on the system’s dynamics. This modification allow a verification to be made of the estimated dynamical characteristics precision. Using the Rossler system in the regime of a phase-coherent chaos we consider features of application of this method to point processes of the integrate-and-fire and the threshold-crossing models.

Reference: 
  1. Bialek W., Rieke F., De Ruyter van Steveninck R.R., and Warland D. Reading a neural code // Science. 1991. Vol. 252. 1854.
  2. Sauer T. Interspike interval embedding of chaotic signals // Chaos. 1995. Vol. 5. 127.
  3. Castro R. and Sauer T. Correlation dimension of attractors through interspike intervals // Phys. Rev. E. 1997. Vol. 55. 287.
  4. Hegger R. and Kantz H. Embedding of sequence of time intervals // Europhys. Lett. 1997. Vol. 38. 267.
  5. Castro R. and Sauer T. Reconstructing chaotic dynamics through spike filters // Phys. Rev. E. 1999. Vol. 59. 2911.
  6. Racicot D.M. and Longtin A. Interspike interval attractors from chaotically driven neuron models // Physica D. 1997. Vol. 104. 184.
  7. Sauer T. Reconstruction of dynamical system from interspike intervals // Phys. Rev. Lett. 1994. Vol. 72. 3911.
  8. Pavlov A.N., Sosnovtseva O.V., Mosekilde E., and Anishchenko V.S. Extracting dynamics from threshold-crossing interspike intervals: Possibilities and limitations // Phys. Rev. E. 2000. Vol. 61. 5033.
  9. Pavlov A.N., Sosnovtseva O.V., Mosekilde E., and Anishchenko V.S. Chaotic dynamics from interspike intervals // Phys. Rev. E. 2001. Vol. 63. 036205.
  10. Sauer T., Yorke J.A., and Casdagli M. Embedology // J. Stat. Phys. 1991. Vol. 65. 579.
  11. Wolf A., Swift J.B., Swinney H.L., and Vastano J.A. Determining Lyapunov exponents from a time series // Physica D. 1985. Vol. 16. 285.
  12. Janson N.B., Pavlov A.N., Neiman A.B., and Anishchenko V.S. Reconstruction of dynamical and geometrical properties of chaotic attractors from threshold-crossing interspike intervals // Phys. Rev. E. 1998. Voo. 58. R4.
  13. Pavlov A.N., Pavlova O.N., Mohammad Y.K., and Kurths J. Quantifying chaotic dynamics from integrate-and-fire processes // Chaos. 2015. Vol. 25. 013118.
  14. Pavlov A.N., Pavlova O.N., Mohammad Y.K., and Kurths J. Characterization of the chaos–hyperchaos transition based on return times // Phys. Rev. E. 2015. Vol. 91. 022921.
  15. Benettin G., Galgani L., Giorgilli A., and Strelcyn J.M. Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: A method for computing all of them // Meccanica. 1980. Vol. 15. 9.
Received: 
08.11.2015
Accepted: 
07.12.2015
Published: 
29.04.2016
Short text (in English):
(downloads: 58)