Using synchronization of chaos to identify the dynamics of unknown systems.

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 Rössler systems. We also consider the effects of measurement noise and of deviation of our fitting model from consistency with the true dynamics.