Synchronization-Based Parameter Estimation in Chaotic Dynamical Systems

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 Rossler 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.

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