An Interdisciplinary Journal

* 2000, Volume 3, Number 3, pp.268--283*

This paper is about mode interaction in systems of coupled nonlinear
oscillators. That is to say, about the interaction of two "pure" modes via
a mixed motion with a lesser degree of symmetry, in many cases leading
eventually to chaos. This nonlinear interaction is obviously a much more
intricate affair than a simple superposition of the contributing modes,
and we will use group theory to gain some general insight in it. It will
be demonstrated that not just any two modes can interact with each other,
but only those which are linked in the system's symmetry hierarchy by a
common daughter mode; further we shall see that the interaction strongly
depends on the nonlinearities of the system. Our model system consists of
two coupled, parametrically driven pendulums but we also pay attention to
mode interaction in the Faraday experiment (as observed by Ciliberto and
Gollub) and in animal locomotion.

*Key words: *nonlinear oscillators,
coupled parametrically driven pendulums, chaos.

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Last updated: *June 16, 2001*