SYNCHRONIZATION OF UNSTABLE ORBITS USING ADAPTIVE-CONTROL

We propose a method of controlling nonlinear and chaotic systems which is able to synchronize the phase space trajectory to a desired unstab le orbit. The desired orbit could be an unstable periodic orbit or a c haotic orbit. The method uses the procedure of adaptive control and in troduces time dependent changes in the system parameters. The changes in the parameter values depend on the deviations of the variables of t he system from the desired orbit and the deviations of the controlled parameters from their values corresponding to the desired orbit. We il lustrate our method using the Lorenz and Rossler systems. We also show that our method may be useful for communication purposes.