CHAOTIC SYSTEM (Stabilization of a)

Charles François (2004). CHAOTIC SYSTEM (Stabilization of a), International Encyclopedia of Systems and Cybernetics, 2(1): 419.

Collection	International Encyclopedia of Systems and Cybernetics
Year	2004
Vol. (num.)	2(1)
ID	◀ 419 ▶
Object type	Methodology or model

According to Ed. OTT et al. (1990, p.1196), as quoted by D. BROOMHEAD, a chaotic system can be stabilized, at least in the absence of other uncontrolled effects as for example genuine noise “… by repeated application of small perturbations, in a state which approximates the chosen state to within a preset error. By keeping the error small, the magnitude of the perturbation is correspondingly kept below a threshold p* ” (1990, p.23).

However, this is possible only “… when the chaotic wandering has brought the system sufficiently close to the center C (of the saddle of the attractor). It is property of the chaotic attractor that this will happen after an unknown but finite time t” (Ibid.).

See also