Abstract: An actively stabilized random number generator includes a random number generator and a feedback controller. The random number generator includes a chaotic physical circuit realizing an iterated function. The iterated function is configured to produce a trajectory of iterates and has an operating parameter ? and a desired Markov operating point. A binary bit converter has a symbol function configured to produce binary symbols from the trajectory of iterates and a maximal kneading sequence. The feedback controller is configured to observe the maximal kneading sequence within the trajectory of iterates and adjust the operating parameter to the desired Markov operating point.

Abstract: A method and apparatus for communicating with chaotic and other waveforms employs a filter for estimating a parameter that describes a property of a signal. The filter is constructed by defining a system that models the source of the signal. The system is partitioned into a first subsystem that contains the parameter and a second subsystem that does not contain the parameter, the second subsystem including a term that makes the second subsystem stable and synchronizable with the signal. The signal is introduced as input to the second subsystem and an element of the second subsystem is substituted into a corresponding element of the first subsystem, thereby generating a signal-activated subsystem. An integration factor is introduced to the signal-activated subsystem to cause the parameter to behave as a constant when the signal-activated subsystem with the integration factor is integrated with respect to time.

Abstract: A method and apparatus for communicating with chaotic and other waveforms employs a filter for estimating a parameter that describes a property of a signal. The filter is constructed by defining a system that models the source of the signal. The system is partitioned into a first subsystem that contains the parameter and a second subsystem that does not contain the parameter, the second subsystem including a term that makes the second subsystem stable and synchronizable with the signal. The signal is introduced as input to the second subsystem and an element of the second subsystem is substituted into a corresponding element of the first subsystem, thereby generating a signal-activated subsystem. An integration factor is introduced to the signal-activated subsystem to cause the parameter to behave as a constant when the signal-activated subsystem with the integration factor is integrated with respect to time.