## CHAOS (Control of)
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E. OTT and M. SPANO showed that, while "the extreme sensitivity and complex behavior that characterize chaotic systems prohibit long range prediction of their behavior", they paradoxically allow one to control them with tiny perturbations" (1995, p.34).

They explain this stabilization process as follows: "The periodic orbits embedded in a chaotic attractor are all unstable in that if one displaces the system state slightly from a periodic orbit, this displacement grows exponentially with time. Thus periodic orbits are typically not observed in a free running chaotic system". However: "Very infrequently a chaotic orbit may, in its ergodic wandering, approach close to a given periodic orbit. If this happens, the orbit may approximately follow the periodic orbit for a few cycles, but subsequently moves away, resuming its wandering over the chaotic attractor".

The control problem consists in stabilizing these "wanderings" near some selected periodic orbits. To do this the authors state: "We tailor our small time-dependent controls in such a way as to stabilize one of of the unstable periodic orbits that yields improved performance" (p.35-6).

In this way, the ergodic character of the system could be to some extent reduced. (For technical details see this very suggestive paper).

The experimental research, to date, shows the feasibility of chaos control. The authors conclude: "The remaining question is whether it will prove possible to move from laboratory demonstrations on model systems to the real world situations of economics, engineering and societal importance. The ubiquity of chaotic dynamics leads us to suspect that this will indeed be the case" (p.40).

The other remaining question is however if meddling with naturally chaotic systems would necessarily be wise. The rhythm of the heart pulses for example has been proven to be normally slightly chaotic, possibly as this implies adaptive variety to internal and external disturbances. We are in problems when this rhythm becomes too narrowly and regularly periodic. We should beware not let ourselves entramped in our classical semantics, according to which chaos is "bad" or "scandalous" in itself.

### Categories

- 1) General information
- 2) Methodology or model
- 3) Epistemology, ontology and semantics
- 4) Human sciences
- 5) Discipline oriented

### Publisher

Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

* Bertalanffy Center for the Study of Systems Science (2020).* Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

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