A limit-cycle solver for nonautonomous dynamical systems
Dynamical Systems
2007-05-23 v1
Abstract
A numerical technique used to solve boundary value problems is modified to find periodic steady-state solutions of nonautonomous dynamical systems. The technique uses a matrix representation of the time derivative obtained through trigonometric interpolation of a periodic function. Such a differentiation matrix yields exact values for the derivative of a trigonometric polynomial and therefore, can be used as the main ingredient of a numerical method to solve nonlinear dynamical systems. We apply this technique to obtain some limit cycles and bifurcation points of a sinusoidally driven pendulum and the steady-state response of an electric circuit.
Cite
@article{arxiv.math/0306161,
title = {A limit-cycle solver for nonautonomous dynamical systems},
author = {Rafael G. Campos and Gilberto O. Arciniega},
journal= {arXiv preprint arXiv:math/0306161},
year = {2007}
}
Comments
Latex file, 9 pages, 4 figures