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<p>The stochastic resonance (SR) phenomenon for a birhythmic van der Pol (BVDP) system with periodically-varying damping subject to multiplicative and additive noise is studied. Applying stochastic averaging method, the stochastic differential equation of the instantaneous amplitude for the BVDP system is deduced. It is shown that within certain region of the system parameters of the BVDP system, the system can be regarded as a bistable one. The signal-to-noise ratio (SNR) for the system is obtained based on the adiabatic condition and two-state theory. One resonant peak is observed when the SNR changes with the frequency of the periodically-varying damping force. Two peak values occur when the SNR varies with the multiplicative noise intensity. One maximum value appears when the SNR varies with the additive noise strength.</p>

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Resonance Phenomenon for a Birhythmic van der Pol System with Periodically-varying Damping Subject to Multiplicative and Additive Noise

  • 期刊论文

  • 发表日期：

    2026年2月23日

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  • Hanbing Yan,
  • Shiqi Jiang,
  • Hai Peng,
  • Jiefeng Liu,
  • Dingqi Zhang,
  • Yupei Zhu

摘要

The stochastic resonance (SR) phenomenon for a birhythmic van der Pol (BVDP) system with periodically-varying damping subject to multiplicative and additive noise is studied. Applying stochastic averaging method, the stochastic differential equation of the instantaneous amplitude for the BVDP system is deduced. It is shown that within certain region of the system parameters of the BVDP system, the system can be regarded as a bistable one. The signal-to-noise ratio (SNR) for the system is obtained based on the adiabatic condition and two-state theory. One resonant peak is observed when the SNR changes with the frequency of the periodically-varying damping force. Two peak values occur when the SNR varies with the multiplicative noise intensity. One maximum value appears when the SNR varies with the additive noise strength.