Estimating the lyapunov exponents of chaotic time series based on polynomial modelling

M. Ataei, A. Khaki-Sedigh, B. Lohmann

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


The problem of Lyapunov Exponents (LEs) estimation from chaotic data based on Jacobian approach by polynomial models is considered. The optimum embedding dimension of reconstructed attractor is interpreted as suitable order of model. Therefore, based on global polynomial mode ling of system, a novel criterion for selecting the embedding dimension is presented. By considering this dimension as the model order, the best nonlinearity degree of polynomial is estimated. The selected structure is used for local estimating of Jacobians to calculate the LEs. This suitable structure of polynomial model leads to better results and avoids of sporious LEs. Simulation results show the effectiveness of proposed methodology.

Original languageEnglish
Pages (from-to)169-174
Number of pages6
JournalIFAC Proceedings Volumes (IFAC-PapersOnline)
Issue number16
StatePublished - 2003
Externally publishedYes
Event13th IFAC Symposium on System Identification, SYSID 2003 - Rotterdam, Netherlands
Duration: 27 Aug 200329 Aug 2003


  • Chaos
  • Jacobian matrices
  • Lyapunov exponents
  • factorization
  • polynomial models
  • time series


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