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Dynamics of saline oscillator under sinusoidal and bounded noise excitation

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  • Bekoa, D.J. Owono
  • Kenfack, W. Fokou
  • Siewe, M. Siewe

Abstract

In this paper, we investigate the effects of harmonic and bounded noise excitations on the saline oscillator dynamics. To this end, we first of all modify an existing coupled saline oscillators model to account for an external excitation. We next analytically derive the system response to harmonic driving by the mean of the harmonic balance method. Then we study the effects of the excitation amplitude and frequency on the dynamic of a sole oscillator and two coupled oscillators. We find that over a wide range of the excitation parameters, the oscillator exhibits period- T oscillations whose amplitude increases with the excitation amplitude. This result is supported by simulations. Moreover, simulations show that periodically excited saline oscillator mainly exhibits, in addition, subharmonic and quasi-periodic oscillations. The above oscillatory modes are determined by the values of the excitation amplitude and frequency. By the mean of stochastic averaging method and Monte-Carlo simulations, the probabilistic response of the oscillator under bounded noise excitation is determined. We find that the saline oscillator does not display the stochastic P-bifurcation when its physical parameters remain in appropriate ranges. However, we find that the bounded noise excitation affects the oscillation period, midpoint and amplitude. Both harmonic and random excitations can be used to induce oscillations in the parameter region where free oscillations are dead.

Suggested Citation

  • Bekoa, D.J. Owono & Kenfack, W. Fokou & Siewe, M. Siewe, 2022. "Dynamics of saline oscillator under sinusoidal and bounded noise excitation," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922002648
    DOI: 10.1016/j.chaos.2022.112054
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    References listed on IDEAS

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    1. G. Augello & D. Valenti & B. Spagnolo, 2010. "Non-Gaussian noise effects in the dynamics of a short overdamped Josephson junction," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 78(2), pages 225-234, November.
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    3. Fokou Kenfack, W. & Siewe Siewe, M. & Kofane, T.C., 2018. "Sliding motion and bifurcation in saline oscillator’s model and liquid’s density measurement using saline oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 321-331.
    4. Siewe, M. Siewe & Kenfack, W. Fokou & Kofane, T.C., 2019. "Probabilistic response of an electromagnetic transducer with nonlinear magnetic coupling under bounded noise excitation," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 26-35.
    5. Fokou Kenfack, W. & Siewe Siewe, M. & Kofane, T.C., 2016. "Nonlinear dynamics and synchronization of saline oscillator’s model," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 72-82.
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