Solutions of the Force-Free Duffing-van der Pol Oscillator Equation
نویسندگان
چکیده
منابع مشابه
New aspects of integrability of force-free Duffing-van der Pol oscillator and related nonlinear systems
In this letter we show that the force-free Duffing-van der Pol oscillator is completely integrable for a specific parametric choice. We derive a general solution for this parametric choice. Further, we describe a procedure to construct the transformation which removes the time dependent part from the first integral and provide the general solution by quadrature. The procedure is shown to have a...
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In this article, under certain parametric conditions, we study the first integrals of the Duffing-van der Pol-type oscillator equations which include the van der Pol and the Duffing oscillator systems, as particular cases. After making a series of variable transformations and applying the PrellerSinger method, we find the first integrals of the simplified equations without complicated calculati...
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In this paper, we study dynamics in delayed van der Pol–Duffing equation, with particular attention focused on nonresonant double Hopf bifurcation. Both multiple time scales and center manifold reduction methods are applied to obtain the normal forms near a double Hopf critical point. A comparison between these two methods is given to show their equivalence. Bifurcations are classified in a two...
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ژورنال
عنوان ژورنال: International Journal of Differential Equations
سال: 2011
ISSN: 1687-9643,1687-9651
DOI: 10.1155/2011/852919