Bifurcation in a parametrically excited two-degree-of-freedom nonlinear oscillating system with 1:2 internal resonance

DOI10.1007/BF02458560zbMath0961.70017OpenAlexW2328862953MaRDI QIDQ1975405

Jinchen Ji, Yu-Shu Chen

Publication date: 16 May 2001

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02458560

zbMATH Keywords

stabilitymethod of multiple scalesglobal bifurcationparametric resonanceMelnikov methodpitchfork bifurcation2:1 internal resonancecritical parametertwo-degree-of-freedom nonlinear systemfirst-order autonomous ordinary differential equationsSmale horseshoe-type chaos

Mathematics Subject Classification ID

Bifurcations and instability for nonlinear problems in mechanics (70K50) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Parametric resonances for nonlinear problems in mechanics (70K28)

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Cites Work

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• On the existence of chaos in a class of two-degree-of-freedom, damped, strongly parametrically forced mechanical systems with broken \(O(2)\) symmetry
• Global bifurcation and chaos in parametrically forced systems with one-one resonance
• Surface waves in closed basins under principal and autoparametric resonances