A limit-cycle solver for nonautonomous dynamical systems

Authors

  • R.G. Campos
  • G.O. Arciniega

Keywords:

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

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.

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Published

2006-01-01

How to Cite

[1]
R. Campos and G. Arciniega, “A limit-cycle solver for nonautonomous dynamical systems”, Rev. Mex. Fís., vol. 52, no. 3, pp. 267–0, Jan. 2006.

Issue

Vol. 52 No. 3 (2006): Revista Mexicana de Física.

Section

Articles

License

Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.