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Implementation of analog circuit and study of chaotic dynamics in a generalized Duffing-type MEMS resonator

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Abstract

We investigate the nonlinear dynamics of a system of generalized Duffing-type MEMS resonator in the frame of simple analog electronic circuit. A mathematical model formed for the proposed generalized Duffing-type MEMS oscillator in which nonlinearities arising out of two different sources such as mid-plane stretching and electrostatic force can lead to variety of nonlinear phenomena such as period-doubling route, transient chaos and homo-/heteroclinic oscillations. These phenomena were confirmed through detailed numerical investigations such as phase portraits, bifurcation diagram, Poincaré map, Lyapunov exponent spectrum and finite-time Lyapunov exponent. The analog circuit realization for the Duffing-type MEMS resonator is constructed. The numerically simulated results are confirmed in the laboratory experimental observations which are closely matched with each other. The experimentally observed chaotic attractor confirmed through FFT spectrum, 0–1 test and Poincaré cross section. In addition, the robustness of the signal strength is confirmed through signal-to-noise ratio.

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Acknowledgements

The authors would like to acknowledge Miss. A. Sugasini for her experimental assistance. S.S. acknowledges University Grants Commission (UGC) for the financial assistance through RFSMS scheme. K.T. acknowledges DST, Govt. of India, for the financial support through the Grant No. SB/EMEQ-077/2013.

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  1. Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli, Tamilnadu, 620024, India

    S. Sabarathinam & K. Thamilmaran

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  1. S. Sabarathinam
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  2. K. Thamilmaran
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Correspondence to K. Thamilmaran.

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Sabarathinam, S., Thamilmaran, K. Implementation of analog circuit and study of chaotic dynamics in a generalized Duffing-type MEMS resonator. Nonlinear Dyn 87, 2345–2356 (2017). https://doi.org/10.1007/s11071-016-3194-2

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