International Encyclopedia of Systems and Cybernetics

"Any system that executes periodic behavior" (S.H. STROGATZ and I STEWART, 1993, p.68).

These authors give the most simple and classical example, the pendulum and comment that :"… it returns to the same point in space at regular intervals; furthermore, its velocity also rises and falls with (clockwork) regularity". They add: "A simple pendulum consisting of a weight at the end of a string can take any of an infinite number or closed paths through phase space, depending on the height from which it is released ".

This corresponds to the linear or harmonic oscillator mathematical model, related to FOURIER analysis of periodic functions.

Moreover: "Biological systems (and clock pendulums), in constrast, tend to have not only a characteristic period but also a characteristic amplitude. They trace a particular path through phase space, and if some perturbation jolts them out of their accustomed rhythm they soon return to their former path" (Ibid).

However, an oscillator with many interfering frequencies not in harmonic relations behaves – or seems to behave – randomly. This is the case of the forced oscillator, in which the introduction of a perturbation disturbs the regular periodic behavior and induces it in a partly, or totally aperiodic, or chaotic movement.

In complex systems with a supposedly deterministic behavior, such a perturbation normally leads to a greater unpredictability.

S. STROGATZ and colleagues have shown and mathematically proven that collection of oscillators, whose frequency can respond to those around it, will end up in synchrony.

This is a deep and very general discovery which establishes a basic model for the spontaneous emergence of order, out of appearent disorder.

The first observation of synchronization was made by the Dutch physicist Chr. HUYGHENS (1629-1695), between two clocks

→ Belousov Zhabotinsky reaction; Order; Network; Smallworld; Synchronicity