A limit-cycle solver for nonautonomous dynamical systems

Abstract

A numerical technique for finding the limit cycles of nonautonomous dynamical systems is presented. This technique uses a matrix representation of the time derivative obtained through the trigonometric interpolation of periodic functions. This differentiation matrix yields exact values for the derivative of a trigonometric polynomial at uniformly spaced points selected as nodes and can therefore be used as the main ingredient of a numerical method for solving nonlinear dynamical systems. We use this technique to obtain some limit cycles and bifurcation points of a sinusoidally driven pendulum and the steady-state response of an electric circuit.