Switching synchronization in 1-D memristive networks: An exact solution

TL;DR

This paper provides an exact analytical solution for the switching synchronization phenomenon in one-dimensional memristive networks, revealing how memristors switch states and how network parameters influence switching time.

Contribution

It introduces an exact solution to the nonlinear dynamics of memristive networks with arbitrary threshold and switching rate distributions, advancing understanding of their synchronization behavior.

Findings

Voltage across memristors is proportional to their thresholds

Derived a compact expression for network switching time

Exact solution without approximations

Abstract

We study a switching synchronization phenomenon taking place in one-dimensional memristive networks when the memristors switch from the high to low resistance state. It is assumed that the distributions of threshold voltages and switching rates of memristors are arbitrary. Using the Laplace transform, a set of non-linear equations describing the memristors dynamics is solved exactly, without any approximations. The time dependencies of memristances are found and it is shown that the voltage falls across memristors are proportional to their threshold voltages. A compact expression for the network switching time is derived.