Dynamical attractors of memristors and their networks

TL;DR

This paper investigates how memristors and their networks can settle into stable fixed-point attractors under periodic driving, providing a theoretical framework for understanding and tuning their long-term behavior.

Contribution

It introduces a general model for memristor fixed-point attractors, derives key equations, and links attractor identification to potential function minimization, advancing understanding of memristor dynamics.

Findings

Fixed-point attractors can be achieved with periodic pulse driving.

A memristor potential function helps identify attractors.

Attractors depend on internal state variable dynamics.

Abstract

It is shown that the time-averaged dynamics of memristors and their networks periodically driven by alternating-polarity pulses may converge to fixed-point attractors. Starting with a general memristive system model, we derive basic equations describing the fixed-point attractors and investigate attractors in the dynamics of ideal, threshold-type and second-order memristors, and memristive networks. A memristor potential function is introduced, and it is shown that in some cases the attractor identification problem can be mapped to the problem of potential function minimization. Importantly, the fixed-point attractors may only exist if the function describing the internal state dynamics depends on an internal state variable. Our findings may be used to tune the states of analog memristors, and also be relevant to memristive synapses subjected to forward- and back-propagating spikes.