Chaotic Systems Predictability Using Neuro-Fuzzy Systems and Neural Networks with Bred Vectors

  • Pettras Leonardo Bueno dos Santos
  • Haroldo Fraga de Campos Velho
  • Rosangela Cintra
  • Sandra Sandri
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 317)


The predictability of the behavior of chaotic systems is of great importance because many real-world phenomena have some type of chaotic regime. In chaotic systems, small changes in the initial conditions can lead to very different results from the original system trajectory. The prediction of chaotic systems behavior is usually very difficult, particularly in practical applications in which initial conditions are obtained by measurement instruments, very often subject to acquisition errors. Here we use “bred vectors” methodology to generate pairs of input/output that are then used to train Neural Networks and Neuro-Fuzzy Systems. We apply the approach to predict regime change for Lorenz strange attractors and the nonlinear coupled three-waves problem from solar physics.


Chaotic systems Bred vectors Lorenz attractor Three-waves problem Neural networks Neuro-fuzzy systems 



The authors thank FAPESP and CNPq for research support.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Pettras Leonardo Bueno dos Santos
    • 1
  • Haroldo Fraga de Campos Velho
    • 1
  • Rosangela Cintra
    • 1
  • Sandra Sandri
    • 1
  1. 1.The Brazilian National Institute for Space Research (INPE)São José dos CamposBrazil

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