An algorithm for the n Lyapunov exponents of an n -dimensional unknown dynamical system

作者: Ramazan Gencay , W.Davis Dechert

DOI: 10.1016/0167-2789(92)90210-E

关键词:

摘要: Abstract An algorithm for estimating Lyapunov exponents of an unknown dynamical system is designed. The estimates not only the largest but all system. estimation carried out by a multivariate feedforward network technique. We focus our attention on deterministic as well noisy estimation. performance very satisfactory in presence noise with limited number observations.

参考文章(15)
Floris Takens, Detecting strange attractors in turbulence Lecture Notes in Mathematics. ,vol. 898, pp. 366- 381 ,(1981) , 10.1007/BFB0091924
M. S. Raghunathan, A proof of Oseledec’s multiplicative ergodic theorem Israel Journal of Mathematics. ,vol. 32, pp. 356- 362 ,(1979) , 10.1007/BF02760464
J. Kurths, H. Herzel, An attractor in a solar time series Physica D: Nonlinear Phenomena. ,vol. 25, pp. 165- 172 ,(1987) , 10.1016/0167-2789(87)90099-6
J. -P. Eckmann, D. Ruelle, Ergodic theory of chaos and strange attractors Reviews of Modern Physics. ,vol. 57, pp. 617- 656 ,(1985) , 10.1103/REVMODPHYS.57.617
Kurt Hornik, Maxwell Stinchcombe, Halbert White, Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks Neural Networks. ,vol. 3, pp. 551- 560 ,(1990) , 10.1016/0893-6080(90)90005-6
Reggie Brown, Paul Bryant, Henry D. I. Abarbanel, Computing the Lyapunov spectrum of a dynamical system from an observed time series Physical Review A. ,vol. 43, pp. 2787- 2806 ,(1991) , 10.1103/PHYSREVA.43.2787
David Ruelle, Ergodic theory of differentiable dynamical systems Publications Mathématiques de l'IHÉS. ,vol. 50, pp. 27- 58 ,(1979) , 10.1007/BF02684768
S. Ellner, A.R. Gallant, D. McCaffrey, D. Nychka, Convergence rates and data requirements for Jacobian-based estimates of Lyapunov exponents from data Physics Letters A. ,vol. 153, pp. 357- 363 ,(1991) , 10.1016/0375-9601(91)90958-B
John Guckenheimer, Philip Holmes, M. Slemrod, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields ,(1983)