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Delayed feedback control of chaos is well known as an effective method for stabilizing unstable periodic orbits embedded in chaotic attractors. However, it had been shown that the method works only for a certain class of periodic orbits characterized by a finite torsion. Modification based on an unstable delayed feedback controller is proposed in order to overcome this topological limitation. An efficiency of the modified scheme is demonstrated for an unstable fixed point of a simple dynamic model as well as for an unstable periodic orbit of the Lorenz system.

It is shown that synchronization in unidirectionally coupled chaotic systems develops in two stages as the coupling strength is increased. The first stage is characterized by a weak synchronization, i.e., a response system subjected to a driving system undergoes a transition and exhibits a behavior completely insensitive to initial conditions. Further increase of the coupling strength causes the dimension decrease of the overall dynamics and leads finally to a strong synchronization. In this stage, the dimension of the strange attractor in the full phase space of the two systems saturates to the dimension of the driving attractor.