Exactly solvable chaotic circuit

We report the construction and operation of a novel chaotic electronic oscillator for which a detailed model admits an exact analytic solution. The circuit is modeled by a hybrid dynamical system including both a differential equation and discrete switching condition. The analytic solution is written as the linear convolution of a symbol sequence and a fixed basis pulse, similar to that of conventional communications waveforms. Waveform returns sampled at the switching times are shown to be conjugate to a chaotic shift map, effectively proving the existence of chaos in the circuit. We show the analytic solution can be used to accurately reconstruct a measured chaotic waveform, thereby confirming the efficacy of the exactly solvable circuit model.