Optimizing Markovian modeling of chaotic systems with recurrent neural networks

Chaos, Solitons and Fractals

Volumn 37, Issue 5, 2008, Pages 1317-1327

  Cechin, Adelmo L ^a   Pechmann, Denise R ^a   de Oliveira, Luiz P L ^a  

^a UNIVERSIDADE DO VALE DO RIO DOS SINOS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; HIDDEN MARKOV MODELS; ONE DIMENSIONAL; OPTIMIZATION; RECURRENT NEURAL NETWORKS; TIME SERIES ANALYSIS;

LORENZ SYSTEMS; SYSTEM DYNAMICS;

CHAOTIC SYSTEMS;

EID: 40949083470     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.10.018     Document Type: Article

References (11)

1. Abarbanel H.D.I. Analysis of observed chaotic data (1996), Springer, San Diego
2. Cannas B., and Cincotti S. Neural reconstruction of Lorenz attractors by an observable. Chaos, Solitons & Fractals 14 (2002) 81-86
3. Lin T., Horne B.G., Tino P., and Giles C.L. Learning long-term dependencies in NARX recurrent neural networks. IEEE Transact Neural Network 1 6 (1996)
4. Hornik K., Stinchcombe M., and White H. Multilayer feedforward networks are universal approximators. Neural Networks 2 5 (1989) 359-366
5. Hornik K. Approximation capabilities of multilayer feedforward neural networks. Neural Networks 4 2 (1991) 251-257
6. Siegelmann H.T., Horne B.G., and Giles C.L. Computational capabilities of recurrent NARX neural networks. IEEE Transact Syst, Man Cyb - Part B: Cyb 27 2 (1997) 208-215
7. Takens F. Detecting strange attractors in turbulence. Lecture notes in math vol. 898 (1981), Springer Verlag
8. Tronci S., Giona M., and Baratti R. Reconstruction of chaotic time series by neural models: a case study. Neurocomputing 55 (2003) 581-591
9. Mañe R. On the dimension of certain compact invariant sets of nonlinear maps. Lecture Notes in Math 898 (1981)
10. Pollicott M. Lectures on ergodic theory and Pesin theory on compact manifolds. London mathematical society lecture note series vol. 180 (1993), Cambridge University Press
11. Ulam S.M. Problems in modern mathematics (1964), Interscience