A limit-cycle solver for nonautonomous dynamical systems
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| Format: | Artículo científico |
| Sprache: | en |
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Sociedad Mexicana de Física A.C.
2006
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| _version_ | 1876467865948782592 |
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| author | G. O. Arciniega |
| author_facet | G. O. Arciniega |
| contents | A limit-cycle solver for nonautonomous dynamical systems G. O. Arciniega R. G. Campos Física, Astronomía y Matemáticas limit cycles nonlinear circuits differentiation matrices trigonometric polynomials Nonautonomous dynamical systems A numerical technique for finding the limit cycles of nonautonomous dynamical systems is presented. This technique uses a matrix representationof the time derivative obtained through the trigonometric interpolation of periodic functions. This differentiation matrix yields exactvalues for the derivative of a trigonometric polynomial at uniformly spaced points selected as nodes and can therefore be used as the mainingredient of a numerical method for solving nonlinear dynamical systems. We use this technique to obtain some limit cycles and bifurcationpoints of a sinusoidally driven pendulum and the steady-state response of an electric circuit. 2006 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57065111 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.3 Vol.52 |
| format | Artículo científico |
| id | redalyc_57065111 |
| institution | Redalyc |
| language | en |
| publishDate | 2006 |
| publisher | Sociedad Mexicana de Física A.C. |
| spellingShingle | A limit-cycle solver for nonautonomous dynamical systems G. O. Arciniega Física, Astronomía y Matemáticas limit cycles nonlinear circuits differentiation matrices trigonometric polynomials Nonautonomous dynamical systems A limit-cycle solver for nonautonomous dynamical systems G. O. Arciniega R. G. Campos Física, Astronomía y Matemáticas limit cycles nonlinear circuits differentiation matrices trigonometric polynomials Nonautonomous dynamical systems A numerical technique for finding the limit cycles of nonautonomous dynamical systems is presented. This technique uses a matrix representationof the time derivative obtained through the trigonometric interpolation of periodic functions. This differentiation matrix yields exactvalues for the derivative of a trigonometric polynomial at uniformly spaced points selected as nodes and can therefore be used as the mainingredient of a numerical method for solving nonlinear dynamical systems. We use this technique to obtain some limit cycles and bifurcationpoints of a sinusoidally driven pendulum and the steady-state response of an electric circuit. 2006 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57065111 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.3 Vol.52 |
| title | A limit-cycle solver for nonautonomous dynamical systems |
| topic | Física, Astronomía y Matemáticas limit cycles nonlinear circuits differentiation matrices trigonometric polynomials Nonautonomous dynamical systems |
| url | https://www.redalyc.org/articulo.oa?id=57065111 |