# Simplified model and analysis of a pair of coupled thermo-optical MEMS oscillators

## TL;DR

This paper develops a simplified third-order model for coupled thermo-optical MEMS oscillators, analyzing their dynamics and bifurcation structure with analytical and numerical methods.

## Contribution

It introduces a new simplified model capturing key features of thermo-optical MEMS oscillators and analyzes the dynamics of coupled oscillators using analytical techniques.

## Key findings

- Analytical results agree with numerical simulations.
- Bifurcation diagram reveals the system's dynamic transitions.
- Model effectively captures key oscillator behaviors.

## Abstract

Motivated by the dynamics of micro-scale oscillators with thermo-optical feedback, a simplified third order model, capturing the key features of these oscillators is developed, where each oscillator consists of a displacement variable coupled to a temperature variable. Further, the dynamics of a pair of such oscillators coupled via a linear spring is analyzed. The analytical procedures used are the variational equation method and the two-variable expansion method. It is shown that the analytical results are in agreement with the results of numerical integration. The bifurcation structure of the system is revealed through a bifurcation diagram.