A method for generating a chaotic attractor by destabilization

We propose a method for generating a chaotic orbit by using destabilizing control for a stable equilibrium or a stable limit cycle in given differential equation. The controller is designed with the pole assignment technique, which is applied in many linear control systems. In the case of an equilibrium point, the poles of the characteristic equation are located in the right half plane. Control is started when the orbit flows into the point, and is activated during an appropriate interval. Then the orbit is repelled from the point and becomes chaotic. In the case of a limit cycle, the poles of the characteristic equation of the Poincare mapping for a fixed point are assigned as unstable poles. As illustrative examples, a stable equilibrium point of a gradient system, a stable limit cycle of the van der Pol equation, and the extended BVP equation are destabilized and chaotic attractors are obtained. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt. 3, 80(11): 73–81, 1997