Influence of noise on Duffing-Van der Pol oscillators. (English) Zbl 0615.70024
An investigation of Duffing-Van der Pol oscillators excited by white noise is presented in the paper. The authors start from a more principal point of view showing first solution of the stationary Fokker-Planck equation. The procedure is next developed and applied to analysis of stochastic Hopf bifurcation of Duffing-Van der Pol oscillators. As an interesting result is obtained that the classical Hopf bifurcation is essentially modified by the stochastic fluctuations. Also probability distribution has in general no radial symmetry.
In the second part of the paper the computer simulations are presented and local Lyapunov exponents are analyzed. Numerical analysis confirm theoretical results.
The presented observations of Duffing-Van der Pol stochastic oscillations should be of interest for readers working in the nonlinear vibration theory.
In the second part of the paper the computer simulations are presented and local Lyapunov exponents are analyzed. Numerical analysis confirm theoretical results.
The presented observations of Duffing-Van der Pol stochastic oscillations should be of interest for readers working in the nonlinear vibration theory.
Reviewer: J.Wicher
MSC:
| 70L05 | Random vibrations in mechanics of particles and systems |
| 70K20 | Stability for nonlinear problems in mechanics |
| 70F99 | Dynamics of a system of particles, including celestial mechanics |
| 65C99 | Probabilistic methods, stochastic differential equations |
Keywords:
Duffing-Van der Pol oscillators; white noise; stationary Fokker-Planck equation; stochastic Hopf bifurcation; stochastic fluctuations; probability distribution; local Lyapunov exponents; nonlinear vibration theoryReferences:
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