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Duffing-van der Pol-type oscillator systems

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  • In this paper, under certain parametric conditions we are concerned with the first integrals of the Duffing-van der Pol-type oscillator system, which include the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. After applying the method of differentiable dynamics to analyze the bifurcation set and bifurcations of equilibrium points, we use the Lie symmetry reduction method to find two nontrivial infinitesimal generators and use them to construct canonical variables. Through the inverse transformations we obtain the first integrals of the original oscillator system under the given parametric conditions, and some particular cases such as the damped Duffing equation and the van der Pol oscillator system are included accordingly.
    Mathematics Subject Classification: Primary: 34C14, 37G10; Secondary: 34C05.


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