A limit-cycle solver for nonautonomous dynamical systems

R.G. Campos, G.O. Arciniega

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.

Keywords


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

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Revista Mexicana de Física

ISSN: 2683-2224 (on line), 0035-001X (print)

Bimonthly publication of Sociedad Mexicana de Física, A.C.
Departamento de Física, 2o. Piso, Facultad de Ciencias, UNAM.
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Tel/Fax: (52) 55-5622-4946, (52) 55-5622-4840. rmf@ciencias.unam.mx