A novel chaotic oscillator is shown to admit an exact analytic solution and a simple matched filter. The oscillator is a hybrid dynamical system including both a differential equation and a discrete switching condition. The analytic solution is written as a linear convolution of a symbol sequence and a fixed basis function, similar to that of conventional communication waveforms. Waveform returns at switching times are shown to be conjugate to a chaotic shift map, effectively proving the existence of chaos in the system. A matched filter in the form of a delay differential equation is derived for the basis function. Applying the matched filter to a received waveform, the bit error rate for detecting symbols is derived, and explicit closed-form expressions are presented for special cases. The oscillator and matched filter are realized in a low-frequency electronic circuit. Remarkable agreement between the analytic solution and the measured chaotic waveform is observed.

New experimental results demonstrate that chaos control can be accomplished using controllers that are very simple relative to the system being controlled. Chaotic dynamics in a driven pendulum and a double scroll circuit are controlled using an adjustable, passive limiter-a weight for the pendulum and a diode for the circuit. For both experiments, multiple unstable periodic orbits are selectively controlled using minimal perturbations. These physical examples suggest that chaos control can be practically applied to a much wider array of important problems than initially thought possible.

Abstract-In this paper, a new approach for communication using chaotic signals is presented. In this approach, the transmitter contains a chaotic oscillator with a parameter that is modulated by an information signal. The receiver consists of a synchronous chaotic subsystem augmented with a nonlinear filter for recovering the information signal. The general architecture is demonstrated for Lorenz and Rossler systems using numerical simulations. An electronic circuit implementation using Chua's circuit is also reported, which demonstrates the practicality of the approach.

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We demonstrate the use of a chaotic laser pulse train for high-precision ranging. The pulse train is produced by inducing coherence collapse in an AlGaAs semiconductor laser. Measurements of optical spectra, intensity autocorrelation functions, and ladar ranging are presented.