Because of the erratic oscillations in chaotic systems, it is often desirable to control them to a steady state. When a controller is added it creates a new dynamical system whose properties are influenced by the underlying chaotic system. Increasing the amount of control has a dramatic effect on the manifolds and the basin for the desired stable steady state. Therefore, it is important to understand the effect of the unique properties of chaotic systems when developing new controller designs to yield optimum performance.

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