Frequency control of singularly perturbed forced Duffing's oscillator

DOI10.1007/s10883-011-9125-0zbMath1238.34071arXiv1709.01318OpenAlexW2045776800MaRDI QIDQ652652

Marcel Abas, Robert Vrabel

Publication date: 15 December 2011

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.01318

zbMATH Keywords

singular perturbationsforced Duffing's oscillatorlarge frequency oscillationspolar coordinate transformation

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Geometric methods in ordinary differential equations (34A26) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Singular perturbations for ordinary differential equations (34E15)

Related Items (2)

Active control of oscillation patterns in the presence of multiarmed pitchfork structure of the critical manifold of singularly perturbed system ⋮ Duffing-type oscillator with a bounded from above potential in the presence of saddle-center bifurcation and singular perturbation: frequency control

Cites Work

• Unnamed Item
• A generalized KYP Lemma-based approach for \(H _{\infty }\) control of singularly perturbed systems
• Geometric singular perturbation theory for ordinary differential equations
• On the construction of asymptotically optimal controls for singularly perturbed systems
• Introduction to Non-Linear Mechanics. (AM-11)
• Averaging methods in nonlinear dynamical systems
• Relaxation oscillation and canard explosion

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