Journal ArticleDOI
Computation of quasi-periodic solutions of forced dissipative systems II
TLDR
In this article, the problem of finding a T -periodic solution of a forced dissipative system of ordinary differential equations is most conveniently reformulated as a fixed point problem of a Poincare map mapping the phase space at t = 0 into the phase spaces at T = T, and the stability of the periodic response is equivalent to the stability for the fixed point.About:
This article is published in Journal of Computational Physics.The article was published on 1986-06-01. It has received 37 citations till now. The article focuses on the topics: Fixed point & Poincaré map.read more
Citations
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Journal ArticleDOI
Continuation of Quasi-periodic Invariant Tori
TL;DR: A new algorithm for the computation and continuation of quasi-periodic invariant tori of ODEs that is based on a natural parametrization of such tori that requires neither the computation of a base of a transversal bundle nor remeshing during continuation.
Journal ArticleDOI
Stability and non-linear responses of a rotor-bearing system with pedestal looseness
Fulei Chu,Y. Tang +1 more
TL;DR: In this paper, a rotor bearing system with pedestal looseness is investigated and a non-linear mathematical model containing stiffness and damping forces with tri-linear forms is considered, and the shooting method is used to obtain the periodic solutions of the system.
Journal ArticleDOI
An investigation into the fast- and slow-scale instabilities of a single phase bidirectional boost converter
TL;DR: In this article, the authors developed an analytical map for a single phase bidirectional boost converter, which enables the analysis of the dynamics of the converter faster and without any convergence problems.
Journal ArticleDOI
Harmonic Balance-Based Approach for Quasi-Periodic Motions and Stability Analysis
Mikhail Guskov,Fabrice Thouverez +1 more
TL;DR: In this article, the stability of a nonlinear response of a Duffing oscillator under a bi-periodic excitation has been compared with a modified 1D harmonic balance approach.
Journal ArticleDOI
A substitution algorithm for solving nonlinear circuits with multi‐frequency components
TL;DR: In this article, a substitution method for calculating the steady state response of nonlinear circuits such as forced circuits driven by multi-frequency component signals, forced oscillators, and coupled oscillators is presented.
References
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Book
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
TL;DR: In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
J. Guckenheimer,P. J. Holmes +1 more
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Book
Advanced mathematical methods for scientists and engineers
Carl M. Bender,Steven A. Orszag +1 more
TL;DR: A self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations is given in this paper.
Book
Geometrical Methods in the Theory of Ordinary Differential Equations
TL;DR: In the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has Since the author explains basic ideas free from a number of 2nd order odes as discussed by the authors.
Related Papers (5)
Algorithms for computing almost periodic steady-state response of nonlinear systems to multiple input frequencies
Leon O. Chua,Akio Ushida +1 more