Abstract

CAMPOS, R.G.  and  ARCINIEGA, G.O.. A limit-cycle solver for nonautonomous dynamical systems. Rev. mex. fis. [online]. 2006, vol.52, n.3, pp.267-271. ISSN 0035-001X.

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.

Keywords : Nonautonomous dynamical systems; nonlinear circuits; limit cycles; differentiation matrices; trigonometric polynomials.

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