JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (8): 111-117.doi: 10.6040/j.issn.1671-9352.0.2022.538

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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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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

CLC Number: 

  • O211.6

Fig.1

Image of the potential function of a periodic potential system"

Fig.2

Time series diagram of numerical solution of system (1) (V0=0.8, γ=0.4, α=1.5, β=0.8, D=0.1, Q=0.1)"

Fig.3

Curves of SPD function with different system parameters (γ=0.4, α=1.5, β=0.8, D=0.1, Q=0.1)"

Fig.4

Curres of SPD function with different friction coefficients (V0=0.8, α=1.5, β=0.8, D=0.1, Q=0.1)"

Fig.5

Curves of SPD function with different stability indexes(V0=0.8, γ=0.4, β=0.8, D=0.1, Q=0.1)"

Fig.6

Curves of SPD function with different skew parameters(V0=0.8, γ=0.4, α=1.5, D=0.1, Q=0.1)"

Fig.7

Curves of SPD function with different multiplicative noise intensities(V0=0.8, γ=0.4, α=1.5, β=0.8, Q=0.1)"

Fig.8

Curves of SPD function with different additive noise intensities(V0=0.8, γ=0.4, α=1.5, β=0.8, D=0.1)"

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