  We introduce a method to estimate the initial conditions of a mutivariable
dynamical system from a scalar signal. The method is based on a modified
multidimensional Newton-Raphson method which includes the time evolution of the
system. The method can estimate initial conditions of periodic and chaotic
systems and the required length of scalar signal is very small. Also, the
method works even when the conditional Lyapunov exponent is positive. An
important application of our method is that synchronization of two chaotic
signals using a scalar signal becomes trivial and instantaneous.

Chaotic Dynamics