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Stochastic resonance in a monostable system driven by time-delayed feedback

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Abstract

The characteristic of a monostable stochastic resonance system driven by time-delayed feedback is investigated. Under the small-delay approximation theory, the effective potential function of the system is obtained and the influence of system parameters on the shape of the potential function is also discussed. Furthermore, we consider the influence of the input signal on the system and derive the asymmetric bistable potential function. By using the adiabatic approximation theory and the two-state theory, the theoretical expressions of the steady-state probability distribution function, mean first-passage time and signal-to-noise ratio are obtained, which are three excellent metrics to measure the performance of system. Simulation results show that the parameters A, a and τ can motivate the SR phenomenon while β suppresses the SR phenomenon. At last, the numerical simulation results obtained from the original Langevin equation and the effective Langevin equation can verify whether the theoretical derivation is correct.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 61771085, 61671095, 61371164) and the Project of Key Laboratory of Signal and Information Processing of Chongqing (No. CSTC2009CA2003).

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Authors and Affiliations

  1. School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Gang Zhang, Lin Zhou & Tianqi Zhang

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  1. Gang Zhang
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  2. Lin Zhou
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  3. Tianqi Zhang
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Correspondence to Lin Zhou.

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Zhang, G., Zhou, L. & Zhang, T. Stochastic resonance in a monostable system driven by time-delayed feedback. Indian J Phys 95, 99–108 (2021). https://doi.org/10.1007/s12648-019-01676-4

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