Synchronization and Detecting Hidden Frequencies in Time Series of Hyperchaotic System

A method of using discrete wavelet transformation to detect the hidden frequency spectrum in a chaotic time series and at the same time to give the projection of the original attractor is proposed. This is demonstrated by the Rõssler hyperchaotic system. The relationship between its variables and the principle of composing a driving signal for hyperchaotic synchronization are presented. It is easy and accurate to use our method to get a signal of variable z from the time series of variable w so the projection of the original attractor on (z , w ) plane can be given. From the time series of variable y , the signal of x can be obtained accurately. So when variables y and w are taken as the combined driving variables, the synchronization between the sender and receiver can be easily reached. But x and y (or z and w ) are not good combinations, and driving variables combined by them may include more redundancy.