Coupled multi-component systems: A Simple Membrane Model

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We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear modes of coupling a near continuum system to a discrete system using a nonlinear coupling are examined. This numerical model is a first step towards investigating the dynamical behavior of a flexible sheet coupled nonlinearly to a semi-rigid support, a system which could conceivably represent a biological cell membrane with a supporting protein network. General implications for the dynamical behavior of continuum systems coupled nonlinearly to discrete systems are introduced.