Controlling Symbolic Dynamics in an Exact Folded-Band Chaotic Oscillator

Control of symbolic dynamics in exactly solvable chaotic oscillator is investigated and numerically demonstrated. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations exhibit a folded-band topology and are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map. An exact solution is written as a linear convolution of a basis pulse and a discrete binary sequence, from which an exact symbolic dynamics is defined. A dynamic limiter is effectively used to control symbolic dynamics using an analytic inverse coding function.