# Leveraging the chaotic regime of a MEMS oscillator for gas detection

Pomme Hirschauer, Fabrice Mathieu, Isabelle Dufour, Martial Defoort, Bernard Legrand

<figure><img src="image_1.png" /></figure>

## To cite this version:

Pomme Hirschauer, Fabrice Mathieu, Isabelle Dufour, Martial Defoort, Bernard Legrand. Leveraging the chaotic regime of a MEMS oscillator for gas detection. Nonlinear Micro-Nanosystems symposium, May 2025, Marne-la-Vallée, France. hal-05217868

HAL Id: hal-05217868

https://laas.hal.science/hal-05217868v1

Submitted on 21 Aug 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Leveraging the chaotic regime of a MEMS oscillator for gas detection

Pomme HIRSCHAUER<sup>a</sup>, Fabrice MATHIEU<sup>a</sup>, Isabelle DUFOUR<sup>b</sup>, Martial DEFOORT<sup>c</sup>, Bernard LEGRAND<sup>a</sup>

<sup>a</sup>Université de Toulouse, CNRS, LAAS-CNRS, Toulouse, France

<sup>b</sup>Univ. Bordeaux, IMS, UMR 5218, F-33400 Talence, France

<sup>c</sup>Univ. Grenoble Alpes, CNRS, Grenoble INP, TIMA, 38000 Grenoble, France

Abstract

In harsh environments, measurement noise can severely limit the performance of traditional linear sensors. In this work, we propose exploiting the exponential sensitivity of chaotic systems to minute variations in system parameters to overcome these noise-related limitations1. Specifically, we employ a MEMS Duffing resonator operating in a chaotic regime. Chaos is triggered on demand through a modulated driving frequency2, resulting in a mechanical response in both amplitude and phase that displays chaotic behavior. Importantly, within a limited time window—assuming nearly identical initial conditions—the system dynamics remain reproducible. Within this window, any deviations in the trajectory directly reflect changes in the sensor’s environment, which are then amplified by the system’s inherent exponential sensitivity to initial conditions. Crucially, because chaos is deterministic, distinct changes in the initial conditions consistently yield distinct chaotic evolutions, thereby enabling the chaotic patterns to reliably encode information about variations in the physical variable of interest. We demonstrate this concept for the detection of carbon dioxide (CO₂) in nitrogen (N₂): the variation in the gas composition (CO₂:N₂) alters the mixture density, which, in turn, affects the natural resonance frequency of the MEMS device3. Notably, our experiments reveal that the reproducibility time of the chaotic trajectories scales inversely—and monotonously—with the CO₂ concentration, marking a significant milestone for gas sensing using a chaotic regime.

<figure><img src="image_3.png" /><figcaption>Figure 1. a. Measurement cell for gas detection experiments
b. MEMS response in non-linear regime</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 2. a. Chaotic trajectories of the mechanical vibration for reference in black and for gas at different concentrations in color
b. Time of reproducibility of the chaotic trajectories within a 50mV threshold distance to the reference trajectory</figcaption></figure>

1. Wang, G., Chen, D., Lin, J. & Chen, X. The application of chaotic oscillators to weak signal detection. *IEEE Transactions on Industrial Electronics* 46, 440-444 (1999).

2. Defoort, M., Rufer, L., Fesquet, L. & Basrour, S. A dynamical approach to generate chaos in a micromechanical resonator. *Microsyst Nanoeng* 7, 1-11 (2021).

3. Iglesias, L., Boudjiet, M. T. & Dufour, I. Discrimination and concentration measurement of different binary gas mixtures with a simple resonator through viscosity and mass density measurements. *Sensors and Actuators B: Chemical* 285, 487-494 (2019).