›› 2014, Vol. 23 ›› Issue (8): 80503-080503.doi: 10.1088/1674-1056/23/8/080503

• GENERAL • 上一篇    下一篇

Stochastic resonance in an over-damped linear oscillator

林丽烽a b, 田艳c, 马洪b   

  1. a College of Computer and Information Sciences, Fujian Agriculture and Forestry Uninversity, Fuzhou 350002, China;
    b Department of Mathematics, Sichuan University, Chengdu 610065, China;
    c School of Sciences, Southwest Petroleum University, Chengdu 610500, China
  • 收稿日期:2013-12-18 修回日期:2014-02-18 出版日期:2014-08-15 发布日期:2014-08-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11171238), the Young Teacher Fund of Fujian Agriculture and Forestry Uninversity, China (Grant No. 2011XJJ23), and the Science and Technology Project of the Education Department of Sichuan Province, China (Grant No. 14ZA0050).

Stochastic resonance in an over-damped linear oscillator

Lin Li-Feng (林丽烽)a b, Tian Yan (田艳)c, Ma Hong (马洪)b   

  1. a College of Computer and Information Sciences, Fujian Agriculture and Forestry Uninversity, Fuzhou 350002, China;
    b Department of Mathematics, Sichuan University, Chengdu 610065, China;
    c School of Sciences, Southwest Petroleum University, Chengdu 610500, China
  • Received:2013-12-18 Revised:2014-02-18 Online:2014-08-15 Published:2014-08-15
  • Contact: Ma Hong E-mail:mahong@scu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11171238), the Young Teacher Fund of Fujian Agriculture and Forestry Uninversity, China (Grant No. 2011XJJ23), and the Science and Technology Project of the Education Department of Sichuan Province, China (Grant No. 14ZA0050).

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摘要： For an over-damped linear system subjected to both parametric excitation of colored noise and external excitation of periodically modulated noise, and in the case that the cross-correlation intensity between noises is a time-periodic function, we study the stochastic resonance (SR) in this paper. Using the Shapiro-Loginov formula, we acquire the exact expressions of the first-order and the second-order moments. By the stochastic averaging method, we obtain the analytical expression of the output signal-to-noise ratio (SNR). Meanwhile, we discuss the evolutions of the SNR with the signal frequency, noise intensity, correlation rate of noise, time period, and modulation frequency. We find a new bona fide SR. The evolution of the SNR with the signal frequency presents periodic oscillation, which is not observed in a conventional linear system. We obtain the conventional SR of the SNR with the noise intensity and the correlation rate of noise. We also obtain the SR in a wide sense, in which the evolution of the SNR with time period modulation frequency presents periodic oscillation. We find that the time-periodic modulation of the cross-correlation intensity between noises diversifies the stochastic resonance phenomena and makes this system possess richer dynamic behaviors.

关键词: stochastic resonance, signal-to-noise ratio, periodically modulated noise, cross-correlation intensity between noises

Abstract: For an over-damped linear system subjected to both parametric excitation of colored noise and external excitation of periodically modulated noise, and in the case that the cross-correlation intensity between noises is a time-periodic function, we study the stochastic resonance (SR) in this paper. Using the Shapiro-Loginov formula, we acquire the exact expressions of the first-order and the second-order moments. By the stochastic averaging method, we obtain the analytical expression of the output signal-to-noise ratio (SNR). Meanwhile, we discuss the evolutions of the SNR with the signal frequency, noise intensity, correlation rate of noise, time period, and modulation frequency. We find a new bona fide SR. The evolution of the SNR with the signal frequency presents periodic oscillation, which is not observed in a conventional linear system. We obtain the conventional SR of the SNR with the noise intensity and the correlation rate of noise. We also obtain the SR in a wide sense, in which the evolution of the SNR with time period modulation frequency presents periodic oscillation. We find that the time-periodic modulation of the cross-correlation intensity between noises diversifies the stochastic resonance phenomena and makes this system possess richer dynamic behaviors.

Key words: stochastic resonance, signal-to-noise ratio, periodically modulated noise, cross-correlation intensity between noises

中图分类号:  (Fluctuation phenomena, random processes, noise, and Brownian motion)

  • 05.40.-a
05.40.Ca (Noise) 02.50.-r (Probability theory, stochastic processes, and statistics)