Phase transitions driven by Lévy noise and Gaussian white noise in an asymmetric tristable system

doi:10.3785/j.issn.1008-9497.2024.02.009

Journal of Zhejiang University (Science Edition)

2024, Vol. 51

Issue (2): 205-211 DOI: 10.3785/j.issn.1008-9497.2024.02.009

Physics

Phase transitions driven by Lévy noise and Gaussian white noise in an asymmetric tristable system

Qianru LIU,Yongfeng GUO(

)

School of Mathematics Sciences，Tiangong University，Tianjin 300387，China

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Abstract

In this paper, the phenomenon of phase transition is studied in an asymmetric tristable model driven by Lévy noise and Gaussian white noise. First, the fourth-order Runge-Kutta algorithm is used to simulate the stationary probability density of the system. Then we observe the shape of the stationary probability density curve by adjusting the system parameters and noise parameters. It has been found that asymmetric parameter, additive noise intensity, multiplicative noise intensity, the stability index, and the skewness parameter can all induce phase transition. Moreover, the influence of additive noise intensity and multiplicative noise intensity on the number and height of stationary probability density peaks is opposite. We also found that under the same asymmetric parameters, the influence of positive and negative skewness parameters on the stationary probability density is different.

Key words： asymmetric tristable system Lévy noise stationary probability density noise noise induced phase transition

Received: 13 December 2021 Published: 08 March 2024

CLC:

O 414.2

Corresponding Authors: Yongfeng GUO E-mail: sdjnwsgyf@163.com

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Cite this article:

Qianru LIU,Yongfeng GUO. Phase transitions driven by Lévy noise and Gaussian white noise in an asymmetric tristable system. Journal of Zhejiang University (Science Edition), 2024, 51(2): 205-211.

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https://www.zjujournals.com/sci/EN/Y2024/V51/I2/205

Lévy噪声和高斯白噪声驱动的非对称三稳系统的相转移问题研究

讨论了非对称三稳系统在Lévy噪声和高斯白噪声共同驱动下的相转移问题。采用四阶Runge-Kutta算法，计算了系统的稳态概率密度函数，通过改变系统参数和噪声参数观察其稳态概率密度函数曲线形态的变化情况。研究发现，非对称参数、加性噪声强度、乘性噪声强度、稳定性指标、偏斜参数均可诱导系统相转移，当分别改变加性噪声强度和乘性噪声强度时，概率密度函数的峰数与高度的变化情况相反。此外，在相同的非对称参数下，随着偏斜参数正负取值的变化，概率密度曲线图中峰的结构亦呈现不同的现象。

关键词： 非对称三稳系统, Lévy噪声, 稳态概率密度, 噪声诱导相变

Fig.1 Potential functions under different asymmetric parameters

Fig.2 Response solution of three stable systems

Fig.3 The

P s t (x)

with different values for asymmetric parameters

r

Fig.4 The

P s t (x)

with different values for multiplicative noise intensity

D

Fig.5 The

P s t (x)

with different values for additive noise intensity

Q

Fig.6 The

P s t (x)

with different values for stability index

α

Fig.7 The

P s t (x)

with different values for skewness parameter β


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