TY - JOUR
T1 - The most probable response of some prototypical stochastic nonlinear dynamical systems
AU - Han, Ping
AU - Xu, Wei
AU - Wang, Liang
AU - Ma, Shichao
N1 - Publisher Copyright:
© 2020
PY - 2020/3
Y1 - 2020/3
N2 - The response of the stochastic system hardly provides useful information for researching its characteristic. Therefore, the paper is aimed at utilizing a deterministic tool, namely, the most probable response, to explore the stochastic nonlinear system. Firstly, one defines the most probable response of the stochastic system. Then, its analytical solution is derived by incorporating the extremum theory into the associated Fokker–Planck equation. Finally, two examples are given to illustrate respectively the implication of this method. Meanwhile, it can conclude that the large the intensity of multiplicative noise is, the more obvious the impact is on the response of nonlinear system. However, no matter how the intensity of additive noise changes, the most probable response does not change. The numerical method verifies the validity of analytical solution.
AB - The response of the stochastic system hardly provides useful information for researching its characteristic. Therefore, the paper is aimed at utilizing a deterministic tool, namely, the most probable response, to explore the stochastic nonlinear system. Firstly, one defines the most probable response of the stochastic system. Then, its analytical solution is derived by incorporating the extremum theory into the associated Fokker–Planck equation. Finally, two examples are given to illustrate respectively the implication of this method. Meanwhile, it can conclude that the large the intensity of multiplicative noise is, the more obvious the impact is on the response of nonlinear system. However, no matter how the intensity of additive noise changes, the most probable response does not change. The numerical method verifies the validity of analytical solution.
KW - Fokker–Planck equation
KW - Stochastic systems
KW - The extremum theory
KW - The most probable response
UR - http://www.scopus.com/inward/record.url?scp=85078878128&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2020.109612
DO - 10.1016/j.chaos.2020.109612
M3 - 文章
AN - SCOPUS:85078878128
SN - 0960-0779
VL - 132
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 109612
ER -