Artículos de revistas
Scientific Visualization Of Poincaré Maps
Registro en:
Computers And Graphics (pergamon). , v. 22, n. 2-3, p. 209 - 216, 1998.
978493
2-s2.0-0032021279
Autor
Wu S.-T.
Campos S.P.
De Aguiar M.A.M.
Institución
Resumen
Poincaré maps have proved to be a valuable tool in the analysis of several dynamical systems modeled by differential equations. These maps are generated by reducing the continuous flow to a two-dimensional discrete dynamics. From a map it is possible to identify the chaos phenomenon in a system under the influence of an external parameter. If this external parameter is variable, one can study the behavior of the system by interpolating the set of corresponding Poincaré maps. Despite its usefulness, the computer graphics work carried out so far has been limited to the display and plot of Poincaré maps. In this paper a prototype for the computer analysis of Poincaré maps is described. We show that, from the point-of-view of computer graphics, we can process Poincaré maps as noisy images. This approach not only facilitates the partition of Poincaré maps into regular and chaotic regions but also offers possibilities of visualizing the continuous evolution of a system by varying the external parameters. Some results are given to illustrate the functionalities of the prototype. © 1998 Elsevier Science Ltd. All rights reserved. 22 2-3 209 216 Eckhardt, B., Yao, D.M., (1993) Physica, D65, p. 100. , and references therein Wu, S.T., Campos, S.P., De Aguiar, A.M.M., Scientific Visualization of Poincaré Maps (1997) Proceedings of the 5th International Conference on Computer Graphics and Visualization, Plzen., pp. 592-601 Poincaré, H., (1899) Les Methodes Nouvelle de la Mechanique Céleste, , Gauthier-Villars, Paris Jordan, D.W., Smith, P., (1987) Nonlinear Ordinary Differential Equations, 2nd Edn., , Section 12.5. Clarendon Press, Oxford Guckenheimer, J., Holmes, P., (1983) Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, , Springer-Verlag, New York Lichtenberg, A.J., Lieberman, M.A., (1983) Regular and Stochastic Motion, , Springer-Verlag, NY Lévy, L.P., Reich, D.H., Pfeiffer, L., West, K., (1993) Physica, B189, p. 204 Ullmo, D., Richter, K., Jalabert, R., (1995) Phys. Rev. Lett., 74, p. 383 Berglund, N., Kunz, H., (1996) J. Stat. Phys., 83, p. 81 De Aguiar, M.A.M., (1996) Phys. Rev., E53, p. 4555 Tiago, M.L., De Carvalho, E.T.O., De Aguiar, M.A.M., (1997) Phys. Rev., E55, p. 65 Zhao, T.C., Overmann, M., http://laue.phys.uwm.edu/pub/xformsPaul, B., http://www.ssec.wisc.edu/brianp/homepagel.htmlPeters R.A. II, ftp://129.59.100.16/pub/morph.tar.ZNeider, J., Davis, T., Woo, M., (1993) OpenGL Programming Guide, , Addison-Wesley Publishing, New York Pedrini, H., (1994) 3D Reconstruction from Transversal Sections of Objects (in Portuguese), , M.Sc. Dissertation, FEE/UNICAMP, Brazil Ekoule, A.B., Peyrin, F.C., Odet, C.L., A triangulation algorithm from arbitrary shaped multiple planar contours (1991) ACM Transactions on Graphics, 10 (2), pp. 182-199 Gonzalez, R., Wintz, P., (1992) Digital Image Processing, , Addison Wesley Publishing Company Zhong, G.-Q., Chua, L.O., Brown, R., Experimental Poincaré Maps from the Twist-and-Flip Circuit (1996) IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 43 (10), pp. 874-879 Wisdom, J., (1983) ICARUS, 56, pp. 51-74 Levison, H.F., Shoemaker, E.M., Shoemaker, C.S., (1997) Nature, 385 (6611), pp. 42-44 Hose, G., Eckhardt, B., Pollak, E., (1989) Phys. Rev., A38, p. 3776 Carnegie, A., Percival, J.C., (1984) J. Phys., A17, p. 801 Bajay, F.A., (1996), Ph.D. Thesis UNICAMP (in Portuguese)