Bifurcations in a Mathieu equation with cubic nonlinearities

DOI10.1016/S0960-0779(01)00226-0zbMath1029.70009OpenAlexW1968095635MaRDI QIDQ1610421

Richard H. Rand, Leslie Ng

Publication date: 19 August 2002

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0960-0779(01)00226-0

zbMATH Keywords

Mathieu equationnumerical integrationperturbation methodcubic nonlinearitysecond-order averagingsoftware AUTO\(2:1\) resonancefirst-order averagingslow-flow equations

Mathematics Subject Classification ID

Bifurcations and instability for nonlinear problems in mechanics (70K50) Computational methods for problems pertaining to mechanics of particles and systems (70-08) Averaging of perturbations for nonlinear problems in mechanics (70K65)

Related Items (19)

Nonlinear Dynamics and Parametric Excitation of Piezo-Micro Biological Sensor ⋮ Modulated amplitude waves in collisionally inhomogeneous Bose-Einstein condensates ⋮ Asymptotic solutions and stability analysis for generalized non-homogeneous Mathieu equation ⋮ Bifurcations and chaos in a periodic time-varying temperature-excited bimetallic shallow shell of revolution ⋮ Pure parametric excitation of a micro cantilever beam actuated by piezoelectric layers ⋮ 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 ⋮ Composite tracking control for a class of uncertain nonlinear control systems with uncertain deadzone nonlinearities ⋮ TRANSITION CURVES AND BIFURCATIONS OF A CLASS OF FRACTIONAL MATHIEU-TYPE EQUATIONS ⋮ Onset and limiting amplitude of yaw instability of a submerged three-tethered buoy ⋮ Comparative vibration analysis of a parametrically nonlinear excited oscillator using HPM and numerical method ⋮ Bifurcations of traveling wave solutions for two coupled variant Boussinesq equations in shallow water waves ⋮ On methods for continuous systems with quadratic, cubic and quartic nonlinearities ⋮ Bifurcations of traveling wave solutions in a compound KdV-type equation ⋮ Existence of periodic solutions for the generalized form of Mathieu equation ⋮ Generalized Parametric Resonance ⋮ On the properties of a class of higher-order Mathieu equations originating from a parametric quantum oscillator ⋮ Bifurcations in a Mathieu equation with cubic nonlinearities. II

Uses Software

• AUTO

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Averaging methods in nonlinear dynamical systems
• Unnamed Item
• Unnamed Item

This page was built for publication: Bifurcations in a Mathieu equation with cubic nonlinearities