Open-loop sustained chaos and control: a manifold approach

Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Aug;66(2 Pt 2):026213. doi: 10.1103/PhysRevE.66.026213. Epub 2002 Aug 27.

Abstract

We present a general method for preserving chaos in nonchaotic parameter regimes as well as preserving periodic behavior in chaotic regimes using a multifrequency phase control. The systems considered are nonlinear systems driven at a base frequency. Multifrequency phase control is defined as the addition of small subharmonic amplitude modulation coupled with a phase shift. By implementing multifrequency control, stable and unstable manifold intersections in postcrisis regimes may be manipulated to sustain chaos as well as to sustain periodic behavior. The theory and a preliminary experiment are demonstrated for a CO2 driven laser.