Taming Chaotic Circuits

Control algorithms that exploit chaotic behavior can vastly improve the performance of many practical and useful systems. The program Perfect Moment is built around a collection of such techniques. It autonomously explores a dynamical system's behavior, using rules embodying theorems and definitions from nonlinear dynamics to zero in on interesting and useful parameter ranges and state-space regions. It then constructs a reference trajectory based on that information and causes the system to follow it. This program and its results are illustrated with several examples, among them the phase-locked loop, where sections of chaotic attractors are used to increase the capture range of the circuit.

Causes and Effects of Chaos

Most of the recent literature on chaos and nonlinear dynamics is written either for popular science magazine readers or for advanced mathematicians. This paper gives a broad introduction to this interesting and rapidly growing field at a level that is between the two. The graphical and analytical tools used in the literature are explained and demonstrated, the rudiments of the current theory are outlined and that theory is discussed in the context of several examples: an electronic circuit, a chemical reaction and a system of satellites in the solar system.