Memristance and transmemristance in multiterminal memristive systems

Memristive devices represent promising building blocks for the development of next-generation memory technologies, computing architectures, and neuromorphic systems. In addition to conventional two-terminal memristive circuits and crossbar array structures, multiterminal memristive systems, where emergent behaviours arise from the mutual interaction of numerous memristive elements, have been explored for neuromorphic data processing and computing applications. In this work, we extend the concept of two-terminal memristive devices to generic multiterminal memristive systems. Beyond its ability to describe the specific case of crossbar arrays, the proposed theoretical framework is also applicable to more complex systems such as self-organizing memristive networks, whose internal state dynamics depend not only on time-varying input signals but also on the spatial distribution of the stimulated terminals. After discussing the notion of memristance in multiterminal devices as the evolution of the system “seen” from the stimulating terminals, we demonstrate that the two-terminal memristive framework can be generalized to the concept of transmemristance when additional, non-stimulating electrodes are used to monitor the system’s evolution. Providing a connection between circuit theory and network science, these concepts are investigated both analytically and experimentally using a theoretical memristive graph model and an experimental memristive system based on self-organizing nanowire networks.