# Memristor Circuits for Simulating Nonlinear Dynamics and Their Periodic Forcing

## TL;DR

This paper demonstrates that memristor circuits can simulate a wide range of nonlinear systems, exhibit complex behaviors like chaos under external forcing, and help analyze system dynamics through circuit theory and mode complexity measures.

## Contribution

It introduces the use of memristor circuits to model nonlinear dynamics, analyze their behavior under forcing, and measure mode complexity, providing new tools for nonlinear system simulation.

## Key findings

- Memristor circuits can simulate diverse nonlinear systems.
- External forcing induces chaos and complex oscillations.
- Operation modes of memristors exhibit higher complexity under forcing.

## Abstract

In this paper, we show that the dynamics of a wide variety of nonlinear systems such as engineering, physical, chemical, biological, and ecological systems, can be simulated or modeled by the dynamics of memristor circuits. It has the advantage that we can apply nonlinear circuit theory to analyze the dynamics of memristor circuits. Applying an external source to these memristor circuits, they exhibit complex behavior, such as chaos and non-periodic oscillation. If the memristor circuits have an integral invariant, they can exhibit quasi-periodic or non-periodic behavior by the sinusoidal forcing. Their behavior greatly depends on the initial conditions, the parameters, and the maximum step size of the numerical integration. Furthermore, an overflow is likely to occur due to the numerical instability in long-time simulations. In order to generate a non-periodic oscillation, we have to choose the initial conditions, the parameters, and the maximum step size, carefully. We also show that we can reconstruct chaotic attractors by using the terminal voltage and current of the memristor. Furthermore, in many memristor circuits, the active memristor switches between passive and active modes of operation, depending on its terminal voltage. We can measure its complexity order by defining the binary coding for the operation modes. By using this coding, we show that in the forced memristor Toda lattice equations, the memristor's operation modes exhibit the higher complexity. Furthermore, in the memristor Chua circuit, the memristor has the special operation modes.