# Transient dynamics of pulse-driven memristors in the presence of a stable fixed point

## TL;DR

This paper analyzes the transient behavior of pulse-driven memristors with stable fixed points, providing analytical solutions for their dynamics and relaxation times, validated by numerical simulations.

## Contribution

It introduces an analytical approach to study the transient dynamics of two types of memristors with stable fixed points under pulse driving.

## Key findings

- Analytical trajectories for Biolek and resistor-threshold memristors are derived.
- Relaxation times to the fixed point are calculated.
- Analytical results match numerical simulations perfectly.

## Abstract

Some memristors are quite interesting from the point of view of dynamical systems. When driven by narrow pulses of alternating polarities, their dynamics has a stable fixed point, which may be useful for future applications. We study the transient dynamics of two types of memristors characterized by a stable fixed point using a time-averaged evolution equation. Time-averaged trajectories of the Biolek window function memristor and resistor-threshold type memristor circuit (an effective memristor) are determined analytically, and the times of relaxation to the stable fixed point are found. Our analytical results are in perfect agreement with the results of numerical simulations.