Dynamics of a two-frequency parametrically driven Duffing oscillator

DOI10.1007/BF02429848zbMath0794.34028OpenAlexW1973430785MaRDI QIDQ1322662

J. F. Heagy, William L. Ditto

Publication date: 29 August 1994

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02429848

zbMATH Keywords

critical exponentchaotic behaviorchaotic attractorMelnikov analysisstable manifoldroute to chaoscrisisstrange nonchaotic attractormagnetoelastic ribbontorus-doubling bifurcationtwo-frequency parametrically driven Duffing oscillatortwo-frequency quasiperiodicity

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear elasticity (74B20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Attractors of solutions to ordinary differential equations (34D45) Parametric resonances for nonlinear problems in mechanics (70K28)

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Cites Work

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• Second-order averaging and chaos in quasiperiodically forced weakly nonlinear oscillators
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Strange attractors that are not chaotic
• Global bifurcations and chaos. Analytical methods
• Crises, sudden changes in chaotic attractors, and transient chaos

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