PERIOD-DOUBLING SEQUENCE
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(2) |
| ID | ◀ 2528 ▶ |
| Object type | Methodology or model |
A succession of period-doubling bifurcations.
Period-doubling was discovered by M. FEIGENBAUM.
An orbit on the trajectory is replaced by another one twice as long at each time-step t, while the time needed for a repetition of any cycle is twice the number of time-steps. The longer the period, the faster the period doubling and the smaller the distance between neighbouring points on the orbit: This is a fractalization process.
In this way the process acquires a growingly random aspect that makes it more and more difficult to observe. A sequence of regular oscillations suddenly gives way to unpredictable behavior, and back again to a new pattern of oscillations, and so on, but within shorter and shorter time spans. The process remains however basically deterministic, at least globally.
A period-doubling sequence is the signature of chaos.
See also
Logistic equation, Renormalization. For more precise information, see JENSEN (1987).