Phase Transitions and Duality in Adiabatic Memristive Networks

The development of neuromorphic systems based on memristive elements - resistors with memory - requires a fundamental understanding of their collective dynamics when organized in networks. Here, we study an experimentally inspired model of two-dimensional disordered memristive networks subject to a slowly ramped voltage and show that they undergo a first-order phase transition in the conductivity for sufficiently high values of memory, as quantified by the memristive ON/OFF ratio. We investigate the consequences of this transition for the memristive current-voltage characteristics both through simulation and theory, and uncover a duality between forward and reverse switching processes that has also been observed in several experimental systems of this sort. Our work sheds considerable light on the statistical properties of memristive networks that are presently studied both for unconventional computing and as models of neural networks.