Jk. John et Re. Amritkar, SYNCHRONIZATION OF UNSTABLE ORBITS USING ADAPTIVE-CONTROL, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 49(6), 1994, pp. 4843-4848
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.