Theoretical Foundations of Memristor Cellular Nonlinear Networks: Memcomputing With Bistable-Like Memristors

This paper presents the theory of a novel memcomputing paradigm based upon a memristive version of standard Cellular Nonlinear Networks. The insertion of a nonvolatile memristor in the circuit of each cell endows the dynamic array with the capability to store and retrieve data into and from the resistance switching memories, obviating the current need for extra memory blocks. Choosing the parameters of each cell circuit so that the memristors may undergo solely sharp transitions between two states, each processing element may be approximately described at any time as one of two first-order systems. Under this assumption, the classical Dynamic Route Map may be employed to synthesise and analyse the data storage and retrieval genes. A new system-theoretic methodology, called Second-Order Dynamic Route Map, is also introduced for the first time in this paper. This technique allows to study the operating principles of arrays with second-order processing elements, as is the case, in the proposed network, if the set up of cell circuit parameters induces analogue memristive dynamics. This paper shows how the novel tool may be adopted to investigate the operating mechanisms of a cellular array with second-order cells, which compute the element-wise logical OR between two binary images.