Estimation of initial conditions from a scalar time series

Details Estimation of initial conditions from a scalar time series Estimation of initial conditions from a scalar time series

2000-02-17

arxiv.org/abs/nlin/0002024v1

Nonlinear Sciences

Chaotic Dynamics

6 pages of revtex with 2 PostScript files for figures; submitted to Phys.Rev.Lett

Scientific paper

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.

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