A study on multistability of CNNs with memristors

The paper considers a class of CNNs, named dynamic-memristor (DM) CNNs, where each cell has an ideal capacitor in parallel to an ideal flux-controlled memristor. It is assumed that during the analog computation the memristor is a dynamic element so that, differently from a standard CNN, a DM-CNN cell is described by a second-order system. The main result is that a DM-CNN is convergent when the interconnection matrix is cycle-symmetric. Such convergent DM-CNNs are potentially useful to accomplish image processing tasks in real time. Advantages intrinsically related to the presence of dynamic memristors during the analog computation are discussed and some main differences with standard CNNs are pointed out. One difference is that the computation of DM-CNNs is based on the time evolution of memristor fluxes, i.e., the processing takes place in the charge-flux domain, instead of the typical voltage-current domain as for a standard CNN. In particular, when a steady state is reached, the capacitor voltages, as well as the other voltages and currents in the DM-CNN vanish. Yet the memristors are able to store in a nonvolatile way the result of the analog computation, i.e., the limiting values of the memristor fluxes