A limit-cycle solver for nonautonomous dynamical systems

Details A limit-cycle solver for nonautonomous dynamical systems A limit-cycle solver for nonautonomous dynamical systems

2003-06-10

arxiv.org/abs/math/0306161v1

Rev. Mex. Fis. 52 (3) 267--271 Junio 2006

Mathematics

Dynamical Systems

Latex file, 9 pages, 4 figures

Scientific paper

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.

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