PERIODIC AND QUASIPERIODIC MOTION

Charles François (2004). PERIODIC AND QUASIPERIODIC MOTION, International Encyclopedia of Systems and Cybernetics, 2(2): 2529.

Collection	International Encyclopedia of Systems and Cybernetics
Year	2004
Vol. (num.)	2(2)
ID	◀ 2529 ▶
Object type	Methodology or model

“The combination of two independent periodic motions produces a toric attractor. A quasiperiodic orbit winds itself round the torus like cotton on a bobbin” (I. STEWART, 1989, p.45).

More than two independent periodic motions generally produce, when combined, a chaotic behavior. In J.P. ECKMANN's words, in such case the system may explore “in several occasions the same instability without periodicity” (1992, p.113)… Or possibly, periodicity is so complex and at such a long time scale that it becomes practically unobservable.

P. BERGÉ and M. DUBOIS describe the “three principal ways that may lead to chaos starting from a periodic regime:

“1. by period doubling, for which period is doubled at each bifurcation until nearing a period of infinite length;

“2. By intermittences, for which periodic states slowly destabilize until there is a ”puff“ of turbulence;

“3. by quasi-periodicity, for which the nonlinear interaction of 2 (or 3) oscillators leads to chaotic behavior” (1992, p.128).

See also