Title :
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
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;
Conference_Titel :
Control and Decision Conference (CCDC), 2012 24th Chinese
Conference_Location :
Taiyuan
Print_ISBN :
978-1-4577-2073-4
DOI :
10.1109/CCDC.2012.6244229
