Tracking sustained chaos

A controller for the operation of a nonlinear system responsive to parametric signals for sustaining and tracking a chaotic system, said controller comprising:

• a monitor for detecting an output value from the nonlinear system;
• a processor for calculating iterations of a function representing the nonlinear system as a function of a parametric value and said output value;
• said processor operable to perform parameter perturbations to generate a new parametric value if a current iteration falls within a predetermined neighborhood of a previous iteration;
• and
• an input device for applying said parametric value to the nonlinear system.

A system for controlling the operation of a nonlinear system, said system comprising:

• means for generating a parametric signal having a parametric value;
• and
• controlling means responsive to the parametric signal for controlling the nonlinear system, said controlling means comprising:
• 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 having an output value;
• means responsive to said output signal for producing said feedback signal;
• correcting means, operable when a current iteration of a function representing the nonlinear dynamic system in terms of said parametric value and said output value falls within a predetermined neighborhood of a previous iteration, for performing parameter perturbations to vary said feedback signal.

A system for tracking chaos, said system comprising:

• a nonlinear system having means for generating a parametric signal at an initial time with an initial selected value and at least one subsequent time with at least one subsequent value different from said initial value;
• and
• means responsive to said parametric signal for controlling the nonlinear system at said initial time and at said at least one subsequent time, said controlling means comprising:
• a modulator responsive to said 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;
• and
• means responsive to said output signal for producing and varying said feedback signal when a current iteration of a function representing the nonlinear dynamic system in terms of a value of said parametric signal and a value of said output signal falls within a predetermined neighborhood of a previous iteration.