Coupled multi-component systems: A simple membrane model.

We present initial results regarding the existence, stability and interactionof linear and nonlinear vibrational modes in a system of two coupled, onedimensional lattices with unequal numbers of masses. The effects on thesenonlinear modes of coupling a near continuum system to a discrete systemusing a nonlinear coupling are examined. This numerical model is a firststep towards investigating the dynamical behavior of a flexible sheetcoupled nonlinearly to a semi-rigid support, a system which couldconceivably represent a biological cell membrane with a supporting proteinnetwork. General implications for the dynamical behavior of continuumsystems coupled nonlinearly to discrete systems are introduced.