SCIENTIFIC VISUALIZATION OF POINCARE MAPS

Poincare maps have proved to be a valuable tool in the analysis of sev eral dynamical systems modeled by differential equations. These maps a re generated by reducing the continuous flow to a two dimensional disc rete dynamics. From a map it is possible to identify the chaos phenome non in a system under the influence of an external parameter. If this external parameter is variable, one can study the behavior of the syst em by interpolating the set of corresponding Poincare maps. Despite it s usefulness, the computer graphics work carried out so far has been l imited to the display and plot of Poincare maps. In this paper a proto type for the computer analysis of Poincare maps is described. We show that, from the point-of-view of computer graphics, we can process Poin care maps as noisy images. This approach not only facilitates the part ition of Poincare maps into regular and chaotic regions but also offer s 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. (C) 1998 Elsevier Science Ltd. All rights reserved.