The Duffing–Van der Pol Equation: Metamorphoses of Resonance Curves
نویسنده
چکیده
We study dynamics of the Duffing–Van der Pol driven oscillator. Periodic steady-state solutions of the corresponding equation are determined within the Krylov-Bogoliubov-Mitropolsky approach to yield dependence of amplitude on forcing frequency as an implicit function, referred to as resonance curve or amplitude profile. Equations for singular points of resonance curves are solved exactly. We investigate metamorphoses of the computed amplitude profiles induced by changes of control parameters near singular points of these curves since qualitative changes of dynamics occur in neighbourhoods of singular points. More exactly, conditions for birth of resonances as well as for attractor crises are found. Bifurcation diagrams are computed to show good agreement with theoretical analysis.
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تاریخ انتشار 2015