Related Experiment Video
Updated: May 31, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Stochastic bifurcations in a bistable Duffing-Van der Pol oscillator with colored noise
Yong Xu1, Rencai Gu, Huiqing Zhang
1Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China. hsux3@nwpu.edu.cn
Abstract:
This paper aims to investigate Gaussian colored-noise-induced stochastic bifurcations and the dynamical influence of correlation time and noise intensity in a bistable Duffing-Van der Pol oscillator. By using the stochastic averaging method, theoretically, one can obtain the stationary probability density function of amplitude for the Duffing-Van der Pol oscillator and can reveal interesting dynamics under the influence of Gaussian colored noise. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that system parameters, noise intensity, and noise correlation time, respectively, can be treated as bifurcation parameters. They also imply that the effects of multiplicative noise are rather different from that of additive noise. The results of direct numerical simulation verify the effectiveness of the theoretical analysis. Moreover, the largest Lyapunov exponent calculations indicate that P and D bifurcations have no direct connection.
Related Concept Videos
Types of Damping
Second Order systems II
If ζ...
Damped Oscillations
Although friction and other non-conservative...
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Limits with Oscillating Discontinuities
Forced Oscillations
