Using synchronization of chaos to identify the dynamics of unknown systems

TL;DR

This paper introduces an adaptive synchronization method to identify the equations and parameters of unknown chaotic systems, demonstrated on Lorenz and Rössler models, even with noise and model deviations.

Contribution

It presents a novel adaptive synchronization approach for system identification of chaotic dynamics, handling parameter drift and measurement noise.

Findings

Successfully identified Lorenz and Rössler systems

Effective in noisy environments

Robust against model deviations

Abstract

We address the issue of how to identify the equations of a largely unknown chaotic system from knowledge about its state evolution. The technique can be applied to the estimation of parameters that drift slowly with time. To accomplish this, we propose an adaptive strategy that aims at synchronizing the unknown real system with another system whose parameters are adaptively evolved to converge on those of the real one. Our proposed strategy is tested to identify the equations of the Lorenz and the Rossler systems. We also consider the effects of measurement noise and of deviation of our fitting model from consistency with the true dynamics.