The Reconstruction Technology Based on Nonlinear Chaotic Time Series and Its Applications

There exist two difficulties in how to recognize a system with complex structure. One is that the system itself is complicated. The other is that in general we gather the time series of some state of the system only by some “observer”. Hence, we need a technique that to a great degree can be used to “recover” the global behavior of systems. It includes many important research links: the determination of the chaotic characteristics of time series and the dimension of the dynamical system the time series lies in, the establishment of the basic coordinate frame work of dynamical system; the separation of noise dynamics in this frame work and studies on prediction and macroscopic control on this base. This chapter will present some of the recent studies of the authors and the related results achieved in realizing the key technique.