Anticipatory synchronization via low-dimensional filters

An anticipatory chaotic synchronization scheme based on a low-order all-pass filter is proposed. The filter is designed as a Padé approximation to the transfer function of an ideal delay line, which is used in a standard Voss scheme. We show that despite its simplicity, the filter works in an anticipatory scheme as well as an ideal delay line. It provides extremely small synchronization error in the whole interval of anticipation time where the anticipatory manifold is stable. The efficacy of our scheme is explained by an analytically solvable model of unidirectionally coupled unstable spirals and confirmed numerically by an example of unidirectionally coupled chaotic Rössler systems.