Using continuous control for amplification and displacement of chaotic signals

Continuous control, used on chaotic systems that bear some special symmetries, gives rise to interesting generalized synchronization behaviors which include modification of signal amplitudes, and trajectories of the system being controlled that reproduce the controller attractor in a region of phase space out of the region where it is stable. Theoretical reasoning and computer simulations show how continuous control methods can be used to obtain these generalized synchronization behaviors, and to tune the desired degree of amplification or displacement. Moreover it is shown that these behaviors can be asymptotically stable, and very robust against external noise and mismatches in the controlling arrangement.