title: Exact folded-band chaotic oscillator.
abstract: An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.
authors: U. S. Army RDECOM, RDMR-WSS, Redstone Arsenal, Alabama 35898, USA. ned.corron@us.army.mil
authors: Ned J
authors: NJ
authors: Corron
authors: Jonathan N
authors: JN
authors: Blakely