Amplitude equations for stored spatially heterogeneous states
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.
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