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The First-Integral Method For Duffing-Van Der Pol-Type Oscillator System, Xiaochuan Hu
The First-Integral Method For Duffing-Van Der Pol-Type Oscillator System, Xiaochuan Hu
Theses and Dissertations - UTB/UTPA
In this thesis, we restrict our attention to nonlinear Duffing–van der Pol–type oscillator system by means of the First-integral method. This system has physical relevance as a model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. Firstly we apply the Division Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to explore a quasi-polynomial first integral to an equivalent autonomous system. Then through a certain parametric condition, we derive a more general first integral of the Duffing–van …