The threshold, or saturation phenomenon of spa- tially coupled systems is
revisited in the light of Lyapunov’s theory of dynamical systems. It is shown
that an application of Lyapunov’s direct method can be used to quantitatively
describe the threshold phenomenon, prove convergence, and compute threshold
values. This provides a general proof methodology for the various systems
recently studied. Examples of spatially coupled systems are given and their
thresholds are computed.