Analytical solutions of periodic motions in 1-dimensional nonlinear systems

DOI10.1016/j.chaos.2017.02.003zbMath1380.34066OpenAlexW2586993623MaRDI QIDQ1693930

Albert C. J. Luo, Yeyin Xu, Zhaobo Chen

Publication date: 1 February 2018

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

Full work available at URL: https://doi.org/10.1016/j.chaos.2017.02.003

zbMATH Keywords

stabilityanalytical solutionsbifurcationsperiodic motionsfrequency-amplitude characteristicsone-dimensional nonlinear systems

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Explicit solutions, first integrals of ordinary differential equations (34A05) Numerical problems in dynamical systems (65P99)

Related Items (3)

Numerical and experimental study of the preload induced period-1 and chaotic vibration of a rotor system considering contact effects ⋮ Accurate Explicit Analytical Solutions of the Duffing-Harmonic Oscillator Equation using Nonlinear Time Transformation ⋮ Analytical periodic motions for a first-order nonlinear circuit system under different excitations

Cites Work

• Existence and monotone method for periodic solutions of first-order differential equations
• A generalized upper and lower solutions method and multiplicity results for nonlinear first-order ordinary differential equations
• Exact multiplicity for periodic solutions of a first-order differential equation
• On the symmetry of solutions in non-smooth dynamical systems with two constraints
• Period-m Motions and Bifurcation Trees in a Periodically Excited, Quadratic Nonlinear Oscillator
• ANALYTICAL DYNAMICS OF PERIOD-m FLOWS AND CHAOS IN NONLINEAR SYSTEMS
• Analytical Routes of Period-1 Motions to Chaos in a Periodically Forced Duffing Oscillator with a Twin-well Potential
• Unstable and Stable Period-m Motions in a Twin-well Potential Duffing Oscillator

This page was built for publication: Analytical solutions of periodic motions in 1-dimensional nonlinear systems