INFERRING MECHANISM FROM TIME-SERIES DATA - DELAY-DIFFERENTIAL EQUATIONS

When there is qualitative information about the underlying professes a nd structure of a dynamical system, it may be possible to infer very a ccurate quantitative information about these processes using only an o utput rime series from the system. We illustrate how this can be accom plished for time series data from a delay-differential equation with a single fixed delay. Our approach exploits modem techniques for non-pa rametric function estimation, is robust to fairly high levels of dynam ic noise and measurement error, and can be extended straightforwardly to more general delay-differential systems and multivariate systems.