Computing 1D discontinuous boundaries of dynamical systems

Author

Li, Qingdu ; Tang, Song ; Feng, Xin

Author_Institution

Inst. for Nonlinear Syst., Chongqing Univ. of Posts & Telecomm, Chongqing, China

fYear

2012

fDate

23-25 May 2012

Firstpage

1427

Lastpage

1430

Abstract

This paper presents a novel searching algorithm to compute discontinuous boundaries of dynamic systems. The algorithm first finds two discontinuous points in the boundary by the Monte Carlo method; then detect the whole boundary from the points by a bisection method. In order to check the effectiveness, the algorithm is verified by two examples with theoretical discontinuous boundaries. As an application, we solve the discontinuity of a Poincare map of the Lorenz system discretized, and also compare our result with the cell-mapping method.

Keywords

Monte Carlo methods; Poincare mapping; sampled data systems; time-varying systems; 1D discontinuous boundaries computing; Lorenz system; Monte Carlo method; Poincare map discontinuity; bisection method; cell-mapping method; discontinuous points; dynamical systems; searching algorithm; whole boundary detection; Algorithm design and analysis; Chaos; Fractals; Heuristic algorithms; Legged locomotion; Monte Carlo methods; Cell-mapping; Discontinuous boundaries; Lorenz system; Poincaré map; State space;

fLanguage

English

Publisher

ieee

Conference_Titel

Control and Decision Conference (CCDC), 2012 24th Chinese

Conference_Location

Taiyuan

Print_ISBN

978-1-4577-2073-4

Type

conf

DOI

10.1109/CCDC.2012.6244229

Filename

6244229