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Perturbation analysis of entrainment in a micromechanical limit cycle oscillator. (English) Zbl 1124.34026
The authors study the dynamics for a periodically excited micromechanical disc-shaped oscillator. The device is operated at parameter values just in the super-critical Hopf bifurcation regime of the unforced system. If the excitation frequency is close to the oscillator limit cycle frequency, the oscillator locks itself onto the excitation signal. If the driving frequency is considerably different from the limit cycle frequency, the oscillator assumes its natural frequency and phase. By sweeping the excitation frequency, a hysteresis effect is observed.
Using the multiple scale technique, the authors reduce the governing equations to a planar autonomous system, which can be studied in phase space.
Investigating the reduced system using the bifurcation software AUTO, the authors obtain a remarkably good agreement between experiments, numerical simulation and bifurcation analysis.

MSC:
34C23 Bifurcation theory for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
34E13 Multiple scale methods for ordinary differential equations
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
Software:
AUTO
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References:
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