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1. Stochastic P-bifurcations In Tri-stable van der Pol- Duffing Oscillator | |||
Hao Ying,Wu zhiqiang | |||
Mechanics 20 December 2012 | |||
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Abstract:This paper aims to investigate the stochastic P-bifurcations in the tri-stable van der Pol-Duffing oscillator with Gauss white noise. By using the stochastic averaging method, the stationary probability density function of amplitude is obtained. Then based on the singularity theory of the deterministic system, the explicit parameter conditions for P-bifurcation are deduced, eleven types of qualitatively different probability density curves are founded. Finally the effects of three coefficients, one for linear damping and two for random excitation strength, are discussed. The results are verified by Monte-Carlo numerical simulations. The method used here is also suitable for other systems' P-bifurcation analysis. | |||
TO cite this article:Hao Ying,Wu zhiqiang. Stochastic P-bifurcations In Tri-stable van der Pol- Duffing Oscillator[OL].[20 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4503911 |
2. Uniformly valid frequency solution of the limit cycle of the Duffing-van der Pol equation | |||
Y.M. Chen,J.K. Liu | |||
Mechanics 05 January 2009 | |||
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Abstract:The limit cycle of the Duffing-van der Pol equation is studied. First, an equivalent equation is obtained by considering the product of the frequency of the limit cycle and the coefficient as an independent parameter . Then, the frequency is obtained as a function of and by solving the equivalent equation via the homotopy analysis method. This function provides us with an algebraic equation in . Solving this algebraic equation, an analytical approximation for the frequency is obtained. Numerical examples show that the attained approximation is very accurate and more importantly uniformly valid for all positive values of . | |||
TO cite this article:Y.M. Chen,J.K. Liu. Uniformly valid frequency solution of the limit cycle of the Duffing-van der Pol equation[OL].[ 5 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27342 |
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