Bifurcation of Positive Periodic Solutions to Micro-Electro-Mechanical Systems

• Zhibo Cheng ^[1] ; Ruina Zhao ^[1] ; Qigang Yuan ^[2]
  1. [1] Henan Polytechnic University

     Henan Polytechnic University

     China

     
  2. [2] North China University of Water Resources and Electric Power
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 1, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper investigates the bifurcation of periodic solutions in a canonical massspring model of electrostatically actuated micro-electro-mechanical systems (MEMS).

    Our analysis provides a partial answer to an open problem proposed by Pedro J.

    Torres. In addition, by performing detailed numerical bifurcation analyses, including bifurcation diagrams, time-series plots, and phase portraits, we illustrate and validate the theoretical findings, thereby revealing the underlying dynamical mechanisms of the bifurcation phenomenon.

• Referencias bibliográficas
  • 1. Algamili, A., Khir, M., Dennis, J., et al.: A review of actuation and sensing mechanisms in mems-based sensor devices. Nanoscale Res. Lett....
  • 2. Ai, S., Pelesko, J.: Dynamics of a canonical electrostatic MEMS/NEMS system. J. Dyn. Differ. Equ. 20, 609–641 (2008)
  • 3. Amster, P., Benevieri, P.: Topological methods for delay and ordinary differential equations, (2024)
  • 4. Cheng, Z., Kong, C., Yuan, Q.: Nonlinear dynamics of periodic solutions in electrostatic MEMS: theory and numerical bifurcation analysis....
  • 5. Feltrin, G., Soverano, E., Zanolin, F.: Periodic solutions to parameter-dependent equations with a φ-Laplacian type operator. Nonlinear...
  • 6. Godoy, J., Hakl, R., Yu, X.: Existence and multiplicity of periodic solutions to differential equations with attractive singularities....
  • 7. Gutiérrez, A., Torres, P.: Non-autonomous saddle-node bifurcation in a canonical electrostatic MEMS. Int. J. Bifurc. Chaos 23, 1350088...
  • 8. Gao, R., Wang, Z., Bai, Z., et al.: Nanomechanics of individual carbon nanotubes from pyrolytically grown arrays. Phys. Rev. Lett. 85,...
  • 9. Hakl, R., Torres, P., Zamora, M.: Periodic solutions of singular second order differential equations: upper and lower functions. Nonlinear...
  • 10. Lyshevski, S.: MEMS and NEMS: systems, devices, and structures, CRC press, (2018)
  • 11. Lu, S., Yu, X., An, Z.: Bifurcation and dynamics of periodic solutions of MEMS model with squeeze film damping. Nonlinear Anal. Real World...
  • 12. Nathanson, H., Newell, W., Wickstrom, R., et al.: The resonant gate transistor. IEEE Trans. Electron Devices 4, 117–133 (1967)
  • 13. Nuñez, D., Perdomo, O., Rivera, A.: On the stability of periodic solutions with defined sign in MEMS via lower and upper solutions. Nonlinear...
  • 14. Taffoti Yolong, V., Woafo, P.: Dynamics of electrostatically actuated micro-electro-mechanical systems: single device and arrays of devices....
  • 15. Torres, P.: Mathematical models with singularities-A zoo of singular creatures. Atlantis Press, Amsterdam (2015)
  • 16. Wang, P.: Bifurcation of equilibria in micromachined elastic structures with electrostatic actuation. Int. J. Bifurc. Chaos 11, 469–482...
  • 17. Yu, X., Lu, S.: A singular periodic ambrosetti-prodi problem of rayleigh equations without coercivity conditions. Commun. Contemp. Math....
  • 18. Younis, M.: MEMS linear and nonlinear statics and dynamics, Springer Science & Business Media, (2011)
  • 19. Yu, X., Yuan, Q., Cheng, Z.: Bifurcation and dynamics of periodic solutions to the Rayleigh-Plesset equation: theory and numerical simulation....
  • 20. Yuan, Q., Cheng, Z., Li, X.: Dynamics of periodic solution to a electrostatic micro-electro-mechanical system. Commun. Nonlinear Sci....
  • 21. Zhang, W., Meng, G.: Nonlinear dynamical system of micro-cantilever under combined parametric and forcing excitations in MEMS. Sensor...
  • 22. Zhang, W., Meng, G., Chen, D.: Stability, nonlinearity and reliability of electrostatically actuated MEMS devices. Sensors 7, 760–796...