Fuzzy descriptor systems and spectral analysis for chaotic time series prediction

  • Masoud Mirmomeni
  • Caro Lucas
  • Masoud Shafiee
  • Babak N. Araabi
  • Elaheh Kamaliha
Original Article


Predicting future behavior of chaotic time series and systems is a challenging area in the literature of nonlinear systems. The prediction accuracy of chaotic time series is extremely dependent on the model and the learning algorithm. In addition, the generalization property of the proposed models trained by limited observations is of great importance. In the past two decades, singular or descriptor systems and related fuzzy descriptor models have been the subjects of interest due to their many practical applications in modeling complex phenomena. In this study fuzzy descriptor models, as a more recent neurofuzzy realization of locally linear descriptor systems, which have led to the introduction of intuitive incremental learning algorithm that is called Generalized Locally Linear Model Tree algorithm, are implemented in their optimal structure to be compared with several other methods. A simple but efficient technique, based on the error indices of multiple validation sets, is used to optimize the number of neurons as well as to prevent over fitting in the incremental learning algorithms. The aim of the paper is to demonstrate the advantages of fuzzy descriptor models and to make a fair comparison between the most successful neural and neurofuzzy approaches in their best structures according to prediction accuracy, generalization, and computational complexity. The Mackey–Glass time series, Lorenz time series (as two well-known classic benchmarks), Darwin sea level pressure time series and long-term prediction of Disturbance Storm Time index, an important index of geomagnetic activity (as two natural chaotic dynamics) are used as practical examples to evaluate the power of the proposed method in long term prediction of chaotic dynamics.


Long term prediction Chaotic time series Singular spectrum analysis Fuzzy descriptor models GLoLiMoT 



The authors wish to thank the “National Space Science Data Center” for using this data set. In addition, the authors wish to thank the anonymous reviewers and the editor in chief for their helpful suggestions, which significantly improved the presentation of our work.


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Copyright information

© Springer-Verlag London Limited 2009

Authors and Affiliations

  • Masoud Mirmomeni
    • 1
    • 4
  • Caro Lucas
    • 1
    • 4
  • Masoud Shafiee
    • 2
  • Babak N. Araabi
    • 1
    • 4
  • Elaheh Kamaliha
    • 3
  1. 1.Control and Intelligent Processing Center of Excellence, School of Electrical and Computer Engineering, College of EngineeringUniversity of TehranTehranIran
  2. 2.Faculty of Electrical EngineeringAmir Kabir University of TechnologyTehranIran
  3. 3.Computer Engineering DepartmentSharif University of TechnologyTehranIran
  4. 4.Institute for Studies in Theoretical Physics and MathematicsSchool of Intelligent SystemsTehranIran

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