FITTING ORDINARY DIFFERENTIAL-EQUATIONS TO CHAOTIC DATA

We address the problem of estimating parameters in systems of ordinary differential equations which give rise to chaotic time series. We claim that the problem is naturally tackled by boundary-value-problem methods. The power of this approach is demonstrated by various examples with ideal as well as noisy data. In particular, Lyapunov exponents can be computed accurately from time series much shorter than those required by previous methods.