Abstract: A control method and system are provided to sustain chaos in a nonlinear dynamic system. A sustained transient that is tracked as a system parameter is substantially varied thereby allowing sustained chaotic transients to exist far away from the crisis parameter values. The method includes targeting points near a chaotic transient once the iterates reach a neighborhood of an undesired attractor. Targeting is done so that the natural dynamics of the system would not engage again the iterations and chaotic motion. A brief parameter fluctuation forces the attractor to be a repeller so that a point which lies on the previously existing chaotic transient can be targeted. Consequently, instead of landing on the attractor, the iterations will reach a region of phase space where a chaotic transient is present, causing the chaotic motion to be reexcited.

Abstract: A control method and system are provided to sustain chaos in a nonlinear dynamic system. A sustained transient that is tracked as a system parameter is substantially varied thereby allowing sustained chaotic transients to exist far away from the crisis parameter values. The method includes targeting points near a chaotic transient once the iterates reach a neighborhood of an undesired attractor. Targeting is done so that the natural dynamics of the system would not engage again the iterations and chaotic motion. A brief parameter fluctuation forces the attractor to be a repeller so that a point which lies on the previously existing chaotic transient can be targeted. Consequently, instead of landing on the attractor, the iterations will reach a region of phase space where a chaotic transient is present, causing the chaotic motion to be reexcited.

Abstract: A control system for tracking the operation of a nonlinear system has two parts: a tracking subsystem and a controlling subsystem. The tracking subsystem generates a parametric signal and the controlling subsystem controls and stabilizes the nonlinear system operating under operating conditions corresponding to that parametric signal. The controlling subsystem includes a modulator responsive to the parametric signal and to a feedback signal for producing and applying an input signal to the nonlinear system to cause the nonlinear system to produce an output signal. The controlling subsystem also includes means responsive to the output signal for producing the feedback signal.