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

  • Richard H. RandEmail author
  • Alan T. Zehnder
  • B. Shayak
  • Aditya Bhaskar
Original paper


Motivated by the dynamics of microscale 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.


Micro-electromechanical systems Limit cycle oscillator Coupled oscillators Perturbation method Bifurcations 



This material is based upon work supported by the National Science Foundation under Grant Number CMMI-1634664. The authors wish to thank Professor John Guckenheimer for advising them on the bifurcations involved in this paper.


Funding has been received from NSF as acknowledged above. The entire research presented here is the authors’ own. No part of this article has been reproduced from other Articles or is under consideration elsewhere.

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Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal rights

Research on human and animal subjects was not necessary for this project.

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All authors consent to submission of this article in its present form.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Theoretical and Applied Mechanics, Sibley School of Mechanical and Aerospace EngineeringCornell UniversityIthacaUSA
  2. 2.Department of MathematicsCornell UniversityIthacaUSA

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