# Bifurcation without parameters in a chaotic system with a memristive element

## TL;DR

This paper explores how memory elements influence chaos in electrical systems, demonstrating that memristive devices can induce bifurcations without changing system parameters, affecting chaotic dynamics.

## Contribution

It introduces a novel experimental and theoretical study of chaotic systems extended with memristive elements, revealing parameter-independent bifurcations affecting chaos.

## Key findings

- Memory causes strong changes in chaotic oscillations.
- Transient silent states disrupt amplitude fluctuations.
- Model reveals slow-fast dynamics driven by memory.

## Abstract

We investigate the effect of memory on a chaotic system experimentally and theoretically. For this purpose, we use Chua's oscillator as an electrical model system showing chaotic dynamics extended by a memory element in form of a double-barrier memristive device. The device consists of Au/NbO$_\text{x}$/Al$_\text{2}$O$_\text{3}$/Al/Nb layers and exhibits strong analog-type resistive changes depending on the history of the charge flow. In the extended system strong changes in the dynamics of chaotic oscillations are observable. The otherwise fluctuating amplitudes of the Chua system are disrupted by transient silent states. After developing a model for Chua's oscillator with a memristive device, the numerical treatment reveals the underling dynamics as driven by the slow-fast dynamics of the memory element. Furthermore, the stabilizing and destabilizing dynamic bifurcations are identified that are passed by the system during its chaotic behavior.