Synchronization-Based Parameter Estimation in Chaotic Dynamical Systems

  • Igor TrpevskiEmail author
  • Daniel Trpevski
  • Lasko Basnarkov
Part of the Understanding Complex Systems book series (UCS)


We examine a method of estimating unknown parameters in models of chaotic dynamical systems by synchronizing the model with the time series measured as output of the system. The method drives the model’s parameters by a set of proper parameter update rules to the true values of the parameters of the modeled system. The theory on how to construct this parameter update rules is given along with simple demonstrations with the Lorenz and Rössler systems. Both the scenario when the output represents the full system of the state, and the case when it is a scalar time series representing a function of the system variables are considered. We demonstrate how to apply the method for estimating the topology of a network of chaotic oscillators. Finally, we illustrate its application to estimating parameters of spatially extended systems that possess translational symmetry with a toy atmospheric model.


Lyapunov Exponent Lyapunov Function Chaotic System Lorenz System Error Dynamic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The work is supported by the European Commission (ERC Grant #266722). The authors thank the editor for his invaluable support and insightful discussions. We thank Gregory Duane for providing the results in Fig. 5.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Igor Trpevski
    • 1
    Email author
  • Daniel Trpevski
    • 1
  • Lasko Basnarkov
    • 2
  1. 1.Macedonian Academy for Sciences and ArtsSkopjeMacedonia
  2. 2.Faculty of Computer Science and EngineeringSkopjeMacedonia

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