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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)"

1 FRONZONI L , MANNELLA R . Stochastic resonance in periodic potentials[J]. Journal of Statistical Physics, 1993, 70 (1): 501- 512.
2 KANG Yanmei . Coherence resonance in subdiffusive fractional Klein-Kramers periodic potential systems without a bifurcation precursor[J]. EPL, 2011, 94 (6): 60005.
doi: 10.1209/0295-5075/94/60005
3 许鹏飞, 公徐路, 李毅伟, 等. 含记忆阻尼函数的周期势系统随机共振[J]. 物理学报, 2022, 71 (8): 32- 42.
XU Pengfei , GONG Xulu , LI Yiwei , et al. Stochastic resonance of periodic potential systems containing memory damping functions[J]. Acta Physica Sinica, 2022, 71 (8): 32- 42.
4 GUO Yongfeng , LOU Xiaojuan , DONG Qiang , et al. Dynamic behavior of periodic potential system driven by cross-correlated non-Gaussian noise and Gaussian white noise[J]. International Journal of Robust and Nonlinear Control, 2022, 32 (1): 126- 140.
doi: 10.1002/rnc.5805
5 CHAKRABORTY A . Nonadiabatic tunnelling in an ideal one-dimensional semi-infinite periodic potential system: an analytically solvable model[J]. Molecular Physics, 2011, 109 (3): 429- 434.
doi: 10.1080/00268976.2010.527303
6 QI Qianqian , ZHOU Bingchang . Stochastic resonance in an underdamped periodic potential system with symmetric trichotomous noise[J]. Indian Journal of Physics, 2020, 94 (1): 81- 86.
doi: 10.1007/s12648-019-01421-x
7 LOU Xiaojuan , GUO Yongfeng , DONG Qiang , et al. First-passage behavior of periodic potential system driven by correlated noise[J]. Chinese Journal of Physics, 2020, 68, 270- 283.
doi: 10.1016/j.cjph.2020.09.022
8 GUO Yongfeng , LOU Xiaojuan , DONG Qiang , et al. Stochastic resonance in a periodic potential system driven by cross-correlated noises and periodic signal[J]. International Journal of Modern Physics B, 2019, 33 (28): 1950338.
doi: 10.1142/S0217979219503387
9 NING Lijuan , WANG Jie . Current transport for a spatially periodic potential system with color noises[J]. International Journal of Modern Physics B, 2018, 32 (31): 1850352.
doi: 10.1142/S0217979218503526
10 焦尚彬, 孙迪, 刘丁, 等. α稳定噪声下一类周期势系统的振动共振[J]. 物理学报, 2017, 66 (10): 26- 36.
JIAO Shangbin , SUN Di , LIU Ding , et al. Vibrational resonance of a class of periodic potential systems under α-stable noise[J]. Acta Physica Sinica, 2017, 66 (10): 26- 36.
11 HU Gang . Stochastic resonance in a periodic potential system under a constant force[J]. Physics Letters A, 1993, 174 (3): 247- 249.
doi: 10.1016/0375-9601(93)90767-T
12 刘开贺, 靳艳飞, 马正木. 相关乘性和加性高斯白噪声激励下周期势系统的随机共振[J]. 动力学与控制学报, 2016, 14 (1): 59- 63.
LIU Kaihe , JIN Yanfei , MA Zhengmu . Stochastic resonance of periodic potential systems under correlated multiplicative and additive Gaussian white noise excitation[J]. Journal of Dynamics and Control, 2016, 14 (1): 59- 63.
13 马正木, 靳艳飞. 二值噪声激励下欠阻尼周期势系统的随机共振[J]. 物理学报, 2015, 64 (24): 84- 90.
MA Zhengmu , JIN Yanfei . Stochastic resonance of underdamped periodic potential systems under binary noise excitation[J]. Acta Physica Sinica, 2015, 64 (24): 84- 90.
14 SAIKIA S . The role of damping on stochastic resonance in a periodic potential[J]. Physica A: Statistical Mechanics and Its Applications, 2014, 416, 411- 420.
doi: 10.1016/j.physa.2014.08.060
15 REEBOHN W L , POHLONG S S , MAHATO M C . Periodically driven underdamped periodic and washboard potential systems: dynamical states and stochastic resonance[J]. Physical Review E, 2012, 85 (3): 031144.
doi: 10.1103/PhysRevE.85.031144
16 KHARKONGOR D , REEBOHN W L , MAHATO M C . Particle dynamics in a symmetrically driven underdamped inhomogeneous periodic potential system[J]. Physical Review E, 2016, 94 (2): 022148.
doi: 10.1103/PhysRevE.94.022148
17 JANICKI A , WERON A . Simulation and chaotic behavior of α-stable stochastic processes[M]. New York: Marcel Dekker, 1994: 351- 352.
18 WERON A , WERON R . Computer simulation of Lévy α-stable variables and processes[M]. Karpacz, Poland: Springer, 1995: 379- 392.
19 WERON R . On the Chambers-Mallows-Stuck method for simulating skewed stable random variables[J]. Statistics & Probability Letters, 1996, 28 (2): 165- 171.
20 DYBIEC B , GUDOWSKA N E . Stochastic resonance: the role of α-stable noises[J]. Acta Physica Polonica B, 2006, 37 (5): 1479- 1490.
21 DYBIEC B , GUDOWSKA N E , HANGGI P . Lévy-Brownian motion on finite intervals: mean first passage time analysis[J]. Physical Review E, 2006, 73 (4): 046104.
doi: 10.1103/PhysRevE.73.046104
22 XU Wei , HAO Mengli , GU Xudong , et al. Stochastic resonance induced by Lévy noise in a tumor growth model with periodic treatment[J]. Modern Physics Letters B, 2014, 28 (11): 1450085.
23 HAO Mengli , XU Wei , GU Xudong , et al. Effects of Lévy noise and immune delay on the extinction behavior in a tumor growth model[J]. Chinese Physics B, 2014, 23 (9): 090501.
24 XU Yong , LI Yongge , LI Juanjuan , et al. The phase transition in a bistable duffing system driven by Lévy noise[J]. Journal of Statistical Physics, 2015, 158 (1): 120- 131.
25 顾仁财, 许勇, 张慧清. 非高斯Lévy噪声驱动下的非对称双稳系统的相转移和平均首次穿越时间[J]. 物理学报, 2011, 60 (11): 110514.
GU Rencai , XU Yong , ZHANG Huiqing . Phase transfer and mean first crossing time of asymmetric bistable systems driven by non-Gaussian Lévy noise[J]. Acta Physica Sinica, 2011, 60 (11): 110514.
26 张广丽, 吕希路, 康艳梅. α稳定噪声环境下过阻尼系统中的参数诱导随机共振现象[J]. 物理学报, 2012, 61 (4): 040501.
ZHANG Guangli , LU Xilu , KANG Yanmei . Parameter-induced stochastic resonance phenomena in overdamped systems in α-stable noise environment[J]. Acta Physica Sinica, 2012, 61 (4): 040501.
27 CHEN Can , KANG Yanmei . Dynamics of a stochastic multi-strain SIS epidemic model driven by Lévy noise[J]. Communications in Nonlinear Science and Numerical Simulation, 2017, 42, 379- 395.
28 郭永峰, 王琳杰, 魏芳. Lévy噪声和高斯白噪声共同激励的FHN神经元系统的动力学特性[J]. 应用力学学报, 2019, 36 (4): 806- 811.
GUO Yongfeng , WANG Linjie , WEI Fang . Dynamical properties of FHN neuron system jointly excited by Lévy noise and Gaussian white noise[J]. Chinese Journal of Applied Mechanics, 2019, 36 (4): 806- 811.
29 LI Y G , XU Y , KURTHS J , et al. Levy-noise-induced transport in a rough triple-well potential[J]. Physical Review E, 2016, 94 (4): 042222.
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