TY - JOUR
TI - Transmission dynamics analysis of a bistable Van der Pol oscillator under Gaussian colored noise with fractional inertial element
AU - Li Deying
AU - Li Yajie
AU - Xu Huafeng
AU - Zhang Xiangyun
AU - Chen Shengli
AU - Cheng Feifei
AU - Shi Yue
JN - Thermal Science
PY - 2026
VL - 30
IS - 2
SP - 1259
EP - 1271
PT - Article
AB - The stochastic response and bifurcation phenomenon of system amplitude in a  bi-stable Van der Pol system with fractional inertial element driven by the  Gaussian colored noise is investigated. In the initial step of the process,  the mean square error is minimized, and the harmonic balance technique is  employed. This results in the fractional derivative being found to be  isovalent to a linear combination of inertial and damping forces.  Simultaneously, the original system is simplified to an equivalent integer  order Van der Pol system. Secondly, the steady-state probability density  function of the system amplitude is acquired via stochastic averaging.  According to the principles of singularity theory, the critical parametric  conditions for the stochastic P-bifurcation of system amplitude can be  deter-mined. A qualitative analysis of the stationary PDF curves of  amplitude is finally conducted in each area, with the transition set curves  serving as a dividing point. The congruence between the analytical outcomes  and the numerical results obtained from Monte Carlo simulation and the  radial basis function neural network testifies to the theoretical analysis.  In this paper, the methodology employed and the results obtained can enhance  the design of the fractional-order controller to control the response of  these systems
DO - 10.2298/TSCI2602259L
ER -