Adaptive strategies for recognition, control and synchronization of chaos

We review a series of adaptive algorithms which recognize chaos, stabilize the unstable periodic orbits embedded in a chaotic attractor and synchronize two identical chaotic systems starting from different initial conditions, by exploiting the information of the local contraction or expansion rates of a chaotic system. This adaptive strategy is applied to the chaotic Lorenz, the three- and four-dimensional Rössler and the delayed Mackey-Glass systems.