International Encyclopedia of Systems and Cybernetics

The reinforcement of a complex effect by the periodic coincidence of the different periods of the composing motions.

I. STEWART explains this as follows: "The combined motion repeats exactly if and only if the motions are resonant: there is some period of time that is an exact whole number multiple of each of the separate periods. Usually this doesn't happen" (1989, p.45).

When the respective periods are expressed by prime numbers (as for example 19, 91, 103 and 283) the exact whole number multiple becomes very great and the global periodic coincidence becomes practically unobservable, which does not mecessarily mean that it does not exist.

I. PRIGOGINE states: "Resonance corresponds to the points where the ratio of frequencies is a rational number. Non-resonant points are points where this ratio is irrational" (1989, p.483).

Resonance may thus manifest deterministic chaos by combination of various movements of incommensurable periods.

As an example, resonance between asteroids and planets orbits may lead to orbital instability when the configuration brings the smaller body very close to the bigger one. This is for example the explanation of the perturbing influence of JUPITER on many asteroids and comets (C. MURRAY, 1989, p.61).

A dramatic example has been the destruction of the formerly periodic Levy-Shoemaker 9 comet in 1994, when swallowed by Jupiter.

According to E. JANTSCH resonance is as well basic in mental phenomena: "Between two static forms no exchange of information is possible in free interaction, but between two metabolic forms free interaction can have large qualitative effects. The topological product of two structurally stable systems is generally not structurally stable: the likely degeneration to a stable field leads to resonance" (1975, p.42).

In his study on the "Attentive Brain" S. GROSSBERG proposes a computational approach to resonance, based on the study of a neural network: "Adaptive Resonance Theory". He states: "In an ART neural network, information can flow from short-term to long-term memory during learning or from long-term to short-term memory during recall" (1995, p.440).

This may be the key for explaining the (more or less) markovian or chaotic interrelations between short- and long-term processes in general: long-term is constructed as an accumulative synthesis from short-term movements, but short-term, in the long run is submitted to long-term limits, representative of more general and permanent conditions.