PERIOD-DOUBLING BIFURCATION
Charles François (2004). PERIOD-DOUBLING BIFURCATION, International Encyclopedia of Systems and Cybernetics, 2(2): 2527.
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(2) |
| ID | ◀ 2527 ▶ |
| Object type | Methodology or model |
A threshold in a process that tends to turn chaotic, signaled by the replacement of a period n cycle by a period 2n cycle.
After such a bifurcation the repetition of a certain state of the system needs twice the number of time-steps. When repeated time and again these events are akin to a fractalization of the cycles.
In the case of the logistic equation, as stated by R. JENSEN: “The range of (the parameter) a over which a single cycle is stable decreases rapidly as the period of the cycle increases, which accounts for the rapid accumulation of cycles with larger and larger periods” (1987, p.171).
For $a \ge 3,57$ the global cycle's period becomes infinite.