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加性和乘性三值噪声激励下周期势系统的动力学分析

靳艳飞 王贺强

靳艳飞, 王贺强. 加性和乘性三值噪声激励下周期势系统的动力学分析[J]. 力学学报, 2021, 53(3): 865-873. doi: 10.6052/0459-1879-20-199
引用本文: 靳艳飞, 王贺强. 加性和乘性三值噪声激励下周期势系统的动力学分析[J]. 力学学报, 2021, 53(3): 865-873. doi: 10.6052/0459-1879-20-199
Jin Yanfei, Wang Heqiang. DYNAMICAL ANALYSIS OF A PERIODIC POTENTIAL DRIVEN BY ADDITIVE AND MULTIPLICATIVE TRICHOTOMOUS NOISES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(3): 865-873. doi: 10.6052/0459-1879-20-199
Citation: Jin Yanfei, Wang Heqiang. DYNAMICAL ANALYSIS OF A PERIODIC POTENTIAL DRIVEN BY ADDITIVE AND MULTIPLICATIVE TRICHOTOMOUS NOISES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(3): 865-873. doi: 10.6052/0459-1879-20-199

加性和乘性三值噪声激励下周期势系统的动力学分析

doi: 10.6052/0459-1879-20-199
基金项目: 1) 国家自然科学基金资助项目(12072025);国家自然科学基金资助项目(11772048)
详细信息
    作者简介:

    2) 靳艳飞, 研究员, 主要研究方向: 非线性随机动力学. E-mail: jinyf@bit.edu.cn

    通讯作者:

    靳艳飞

  • 中图分类号: O324,O313

DYNAMICAL ANALYSIS OF A PERIODIC POTENTIAL DRIVEN BY ADDITIVE AND MULTIPLICATIVE TRICHOTOMOUS NOISES

  • 摘要: 周期势系统是一类在机械工程、物理、化学、神经生物等领域应用十分广泛的系统,其随机动力学特性的研究是非线性科学的一个热点和难点问题.三值噪声是真实噪声的典型模型, 不仅包含二值噪声和高斯白噪声情形,而且能更好地描述自然界中随机环境扰动的多样性,本文研究了由加性和乘性三值噪声驱动的周期势系统中概率密度的演化和随机共振.通过计算系统的平均稳态联合概率密度函数和瞬态联合概率密度函数,发现随着外周期力振幅的增大, 单自由度系统在多个稳态之间跃迁,其平均稳态联合概率密度具有多峰结构. 此外,利用随机能量法揭示了系统的随机共振,发现存在最优的噪声强度和外周期力振幅使得平均输入能量曲线存在一个极大值,即出现随机共振现象. 对于仅考虑加性噪声或乘性噪声激励的情况,平均输入能量曲线随噪声转迁率是否出现共振现象依赖于外周期激励振幅的大小.特别是仅考虑加性噪声的情形, 对于较小的外周期激励振幅,加性噪声转迁率诱导产生抑制共振现象, 而对于较大的外周期激励振幅,加性噪声转迁率诱导产生随机共振现象.

     

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出版历程
  • 收稿日期:  2020-06-15
  • 刊出日期:  2021-03-10

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