Nonlinear Phenomena in Complex Systems, 2000, Vol.3, No.3, pp.268--283

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

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

Mode Interaction in a Cup of Coffee and Other Nonlinear Oscillators.
J.P. van der Weele and E.J. Banning

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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