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Stochastic Resonance for an Underdamped Bistable System with Two Kinds of Velocity Time-Delays Subjected to Multiplicative and Additive Noise

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Abstract

The stochastic resonance (SR) phenomenon for an underdamped bistable system with two kinds of velocity time-delays driven by multiplicative and additive noise is investigated. Applying small time-delay approximation, under detailed balance condition, the stationary probability for the system is obtained. The expression for the transition rates out of the two stable states and that for the output signal-to-noise ratio (SNR) of the system are deduced by virtue of two-state theory. Single-peak phenomenon appears when the SNR changes with the velocity time-delays. Traditional SR occurs on the curves of the SNR versus the strengths of the multiplicative and additive noise. A resonance peak takes place when the SNR varies with the damping coefficient. Moreover, it is found that the effects of the two kinds of time-delays and those of the two noises on the SNR are different. The non-monotonous effect of system parameters on the SNR is also investigated.

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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All the results presented in the paper can be reproduced with the information provided in the manuscript.]

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Acknowledgements

Supported by Department of Science and Technology of Sichuan Province under grant (No.2019YFSY0043), by AECC Sichuan Gas Turbine Establishment, by Sichuan Science and Technology Program (No.2020YFG0177, No.2020YFG01770360), and by Key Laboratory on Aero-engine Altitude Simulation Technology.

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Authors and Affiliations

  1. School of Power and Energy, Northwestern Polytechnical University, Xi’an, 710072, China

    Qian Qiu & Zhanxue Wang

  2. Key Laboratory On Aero-Engine Altitude Simulation Technology, Sichuan Gas Turbine Establishment, AECC, Mianyang, 621000, China

    Qian Qiu, Shi-hui Yuan & Xiao-Jiang Shi

  3. School of Control Engineering, Chengdu University of Information Technology, Chengdu, 610225, China

    Shiqi Jiang & Lin Wang

  4. School of Information Engineering, Southwest University of Science and Technology, Mianyang, 621010, China

    Feng Guo

  5. ChongQing College of Electronic Engineering, ChongQing, 401331, China

    Danni Liu

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  1. Qian Qiu
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Contributions

Shiqi Jiang and Qian Qiu completed the numerical simulation and theoretical calculation. Feng Guo wrote the manuscript. The manuscript was revised by Zhanxue Wang, Shihui Yuan, Xiaojiang Shi, Lin Wang, Danni Liu contributed equally to the paper.

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Correspondence to Shiqi Jiang.

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Qiu, Q., Wang, Z., Jiang, S. et al. Stochastic Resonance for an Underdamped Bistable System with Two Kinds of Velocity Time-Delays Subjected to Multiplicative and Additive Noise. Int J Theor Phys 62, 62 (2023). https://doi.org/10.1007/s10773-023-05317-9

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