Abstract :
Pecora and Caroll showed in the case of the Lorenz equation (written in terms of three state variables: X, Y and Z) that two such oscillators can be synchronized with one another by simply sending information about X or Y from one to the other. Since then, this property, called “Chaotic Synchronization”, has also been observed in other systems. We consider a situation in which the sender in some remote location has sent X. The receiver has no knowledge of the initial conditions. The receiver knows that the synchronization will eventually take place, but usually has no idea about the progress of synchronization. One way to solve this problem is to use an additional device which, when connected to the receiving oscillator, will help monitor the progress of synchronization. In fact, using our new algorithm for accurate calculation of derivatives, we can precisely state how far apart the Y and Z states are as they move towards eventual synchronization. In the second part, we use an accurate derivative algorithm to speed up this progress towards synchronization, with or without the aid of the additional component.
