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A limit-cycle solver for nonautonomous dynamical systems

Rafael G. Campos·Gilberto O. Arciniega
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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.

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Rafael G. Campos, Gilberto O. Arciniega. 2003-06-10. A limit-cycle solver for nonautonomous dynamical systems. https://arxiv.org/abs/math/0306161

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