Taming chaotic systems with dithers

A simple approach is proposed to tame chaos by injecting high-frequency signals, commonly called dithers, into the chaotic systems. Based on the relaxed method, an appropriate dither is introduced to suppress chaotic motion. If the frequency of dither is high enough, the trajectory described by the dithered chaotic system and the trajectory of its corresponding mathematical model — the relaxed system would be made as close as desired. This fact enables us to get a rigorous prediction of the dithered chaotic system’s behavior by obtaining the behavior of the relaxed system. Finally, an example with simulations is given to illustrate the concepts discussed throughout this paper.