By introducing memristors into circuit design, the limitations of traditional purely-CMOS hardware may be overcome. However, an extension of standard techniques for the analysis and design of conventional computing structures may be necessary to allow their applicability to the memristive counterparts. This paper adopts a generalization of the Dynamic Route Map system-theoretic concept to elucidate the mechanisms by which bio-inspired arrays of locally-coupled circuits, employing memristors with either bistable-like or analogue dynamic switching behaviours, accomplish image mem-processing tasks through the dynamical evolution of their states toward predefined equilibria.