Bifurcations in a Mathieu equation with cubic nonlinearities. II

DOI10.1016/S1007-5704(02)00018-7zbMath1043.34040OpenAlexW2096312336MaRDI QIDQ1868735

Leslie Ng, Richard H. Rand

Publication date: 28 April 2003

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s1007-5704(02)00018-7

zbMATH Keywords

Mathieu equationnonlinear dynamicsaveraging methodBifurcationsnonautonomous ordinary differential equationsanalytical methods for nonlinear ordinary differential equations

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Averaging method for ordinary differential equations (34C29)

Related Items (8)

Asymptotic solutions and stability analysis for generalized non-homogeneous Mathieu equation ⋮ Stability and torsional vibration analysis of a micro-shaft subjected to an electrostatic parametric excitation using variational iteration method ⋮ Study of parametric oscillation of an electrostatically actuated microbeam using variational iteration method ⋮ An analytical method for Mathieu oscillator based on method of variation of parameter ⋮ Parametric Frequency Analysis of Mathieu–Duffing Equation ⋮ Comparative vibration analysis of a parametrically nonlinear excited oscillator using HPM and numerical method ⋮ Existence of periodic solutions for the generalized form of Mathieu equation ⋮ Generalized Parametric Resonance

Uses Software

• AUTO

Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Bifurcations in a Mathieu equation with cubic nonlinearities
• Nonlinear Mathieu equation and coupled resonance mechanism
• COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
• THE NONLINEAR MATHIEU EQUATION

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