Regensburg 2004 – wissenschaftliches Programm

Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe

DY: Dynamik und Statistische Physik

DY 34: Nonlinear Dynamics and Chaos I

DY 34.4: Vortrag

Mittwoch, 10. März 2004, 15:15–15:30, H2

Recovering the dynamical system from short and contaminated segments of a chaotic trajectory — •Luis Sandoval and Rafael Gutiérrez — Grupo de Sistemas Complejos, Universidad Antonio Nariño, Calle 58A 37-94, Bogotá, Colombia

In this work we determine the sufficient characteristics of a trajectory segment of known chaotic attractors to recover the corresponding dynamical model. The sufficient conditions correspond to: the size of the trajectory segment, the localization of the trajectory segment, and the density of points or sampling frequency. The contamination and resolution of the data points make the sufficient conditions vary. The dynamical models considered have all possible nonlinearities up to order two characterized by thirty parameters. The values of the parameters are obtained from each trajectory segment and then compared with the corresponding values of the known dynamical system with chaotic solutions. In many cases the chaotic solutions are not very sensitive to variations of some parameter values making the comparison of similar but different dynamical systems not well defined in terms of their corresponding chaotic solutions. We solve this problem by using synchronization and estimation of dynamical measures.