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handle: 11380/459598
Summary: The resonance problem and chaotic dynamics, described by the Duffing equation, are reexamined when excitation is external or parametric. Starting from the similarity existing between these two different phenomena, a new concept is introduced: \textit{chaotic resonance}. The proposed idea is confirmed by the analogies between the resonance diagrams and the diagrams of chaotic zones obtained by the Melnikov method. In order to show the generality of this idea, we study a simple case with more than one chaotic resonance.
parametric excitation, resonance diagrams, Duffing equation, diagrams of chaotic zones, Nonlinear dynamics; choas, external excitation, Melnikov method, Nonlinear resonances for nonlinear problems in mechanics, Bifurcations and instability for nonlinear problems in mechanics
parametric excitation, resonance diagrams, Duffing equation, diagrams of chaotic zones, Nonlinear dynamics; choas, external excitation, Melnikov method, Nonlinear resonances for nonlinear problems in mechanics, Bifurcations and instability for nonlinear problems in mechanics
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