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Stochastic resonance phenomenon in an underdamped bistable system driven by weak asymmetric dichotomous noise

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Abstract

Stochastic resonance in an underdamped bistable system subjected to a weak asymmetric dichotomous noise is investigated numerically. Dichotomous noise is a non-Gaussian color noise and more complex than Gaussian white noise, whose waiting time complies with the exponential distribution. Utilizing an efficiently numerical algorithm, we acquire the asymmetric dichotomous noise accurately. Then the system responses and the averaged power spectrum as the signatures of the stochastic resonance are calculated by the fourth-order Runge–Kutta algorithm. The effects of the noise strength, the forcing frequency, and the asymmetry of dichotomous noise on the system responses and the effects of the forcing frequency on the averaged power spectrum are discussed, respectively. It is found that the increasing of the noise strength or the forcing frequency could strengthen the passage between the stable points of the system, and the system responses also display the asymmetry for the asymmetric dichotomous noise, which has not been discovered in other investigated results. Additionally, the averaged power spectrum exhibits the sharp peaks, which indicates the occurrence of stochastic resonance, and we also discover two critical forcing frequencies: one denoting the transformation of the peaks and another for the optimum on stochastic resonance.

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Acknowledgements

This work was supported by the NSF of China (Grant Nos. 10972181, 11102157), Program for New Century Excellent Talents in University, the Shaanxi Project for Young New Star in Science & Technology and NPU Foundation for Fundamental Research.

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, China

    Yong Xu, Juan Wu & Hui-Qing Zhang

  2. School of Information & Computation Science, Beifang University for Nationalities, Yinchuan, 750021, China

    Juan Wu & Shao-Juan Ma

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  1. Yong Xu
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  2. Juan Wu
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Correspondence to Yong Xu.

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Xu, Y., Wu, J., Zhang, HQ. et al. Stochastic resonance phenomenon in an underdamped bistable system driven by weak asymmetric dichotomous noise. Nonlinear Dyn 70, 531–539 (2012). https://doi.org/10.1007/s11071-012-0473-4

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  • DOI: https://doi.org/10.1007/s11071-012-0473-4

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