Memristive networks: from graph theory to statistical physics
A simple solvable model of memristive networks suggests a correspondence between the asymptotic states of memristors and the Ising model.
We provide an introduction to a very specific toy model of memristive networks, for which an exact differential equation for the internal memory which contains the Kirchhoff laws is known. In particular, we highlight how the circuit topology enters the dynamics via an analysis of directed graph. We try to highlight in particular the connection between the asymptotic states of memristors and the Ising model, and the relation to the dynamics and statics of disordered systems.
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A local model of preferential attachment with short-term memory generates scale-free networks, which can be readily computed by memristors.
Exact solutions for the dynamics of interacting memristors predict whether they relax to higher or lower resistance states given random initialisations.
Memristive networks preserve memory and have the ability to learn according to analysis of the network’s internal memory dynamics.
Exact equations of motion provide an analytical description of the evolution and relaxation properties of complex memristive circuits.