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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (8): 111-117.doi: 10.6040/j.issn.1671-9352.0.2022.538

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高斯噪声和Lévy噪声激励下欠阻尼周期势系统的相变行为

丁佳鑫(),郭永峰*(),米丽娜   

  1. 天津工业大学数学科学学院, 天津 300387
  • 收稿日期:2022-10-19 出版日期:2023-08-20 发布日期:2023-07-28
  • 通讯作者: 郭永峰 E-mail:JXDing2333@163.com;guoyongfeng@mail.nwpu.edu.cn
  • 作者简介:丁佳鑫(1999—), 女, 硕士研究生, 研究方向为应用概率统计. E-mail: JXDing2333@163.com
  • 基金资助:
    天津市自然科学基金资助项目(17JCYBJC15700)

Transition behavior of underdamped periodic potential system driven by Gaussian noise and Lévy noise

Jiaxin DING(),Yongfeng GUO*(),Lina MI   

  1. School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
  • Received:2022-10-19 Online:2023-08-20 Published:2023-07-28
  • Contact: Yongfeng GUO E-mail:JXDing2333@163.com;guoyongfeng@mail.nwpu.edu.cn

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摘要：

在研究欠阻尼周期势系统时, 同时引入乘性高斯白噪声和加性Lévy噪声, 首先将二阶欠阻尼周期势系统等价改写为两个一阶随机微分方程, 然后借助Janicki-Weron算法产生Lévy噪声序列, 并通过数值算法进一步模拟出该系统的稳态概率密度函数(steady-state probability density function, SPD), 最后对欠阻尼周期势系统的相变行为进行分析。研究发现系统参数、摩擦系数、稳定性指标、偏斜参数、乘性高斯白噪声强度和加性Lévy噪声强度均可以诱导系统产生相变现象。此外, 系统参数和摩擦系数的增大有利于粒子处于稳定状态。

关键词: 欠阻尼周期势系统, 噪声, 稳态概率密度函数, 相变现象

Abstract:

In the study of an underdamped periodic potential system, multiplicative Gaussian white noise and additive Lévy noise are introduced simultaneously. First, the second-order underdamped periodic potential system is equivalent to two first-order stochastic differential equations. Then, Lévy noise is generated by Janicki-Weron algorithm, the steady-state probability density function of the equation is simulated by the numerical simulation, and the dynamic characteristics of the underdamped periodic potential system are analyzed. It is found that system parameter, friction coefficient, stability index, skew parameter, multiplicative noise intensity and additive Lévy noise intensity can induce phase transition. In addition, it can be observed that the increase of system parameter and the friction coefficient is conducive to the stable state of particles.

Key words: underdamped periodic potential system, noises, steady-state probability density function, transition behavior

中图分类号: 

  • O211.6

图1

周期势系统势函数图像"

图2

系统(1)数值解的时间历程图(V0=0.8, γ=0.4, α=1.5, β=0.8, D=0.1, Q=0.1)"

图3

SPD随不同系统参数变化的曲线(γ=0.4, α=1.5, β=0.8, D=0.1, Q=0.1)"

图4

SPD随不同摩擦系数变化的曲线(V0=0.8, α=1.5, β=0.8, D=0.1, Q=0.1)"

图5

SPD随不同稳定性指标变化的曲线(V0=0.8, γ=0.4, β=0.8, D=0.1, Q=0.1)"

图6

SPD随不同偏斜参数变化的曲线(V0=0.8, γ=0.4, α=1.5, D=0.1, Q=0.1)"

图7

SPD随不同乘性噪声强度变化的曲线(V0=0.8, γ=0.4, α=1.5, β=0.8, Q=0.1)"

图8

SPD随不同加性噪声强度变化的曲线(V0=0.8, γ=0.4, α=1.5, β=0.8, D=0.1)"

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