Amplitude equations for stored spatially heterogeneous states (2506.13576v1)

Abstract: Coupled evolution equations for the amplitudes of heterogeneous states (memories) stored in the connectivity of distributed systems with distance-constrained non-local interactions are derived. The resulting system of coupled amplitude equations describes the spatio-temporal dynamics of the pattern amplitudes. It is shown that these types of distributed systems perform pattern completion and selection, and that the distance restricted connections afford spatio-temporal memory pattern dynamics taking the form of patterning fronts.