TY - JOUR
T1 - Analysis of global properties for dynamical systems by a modified digraph cell mapping method
AU - Yue, Xiaole
AU - Xu, Wei
AU - Zhang, Ying
AU - Du, Lin
N1 - Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2018/6
Y1 - 2018/6
N2 - A modified procedure is proposed in this paper to solve the limitations of digraph cell mapping method in accurately analyzing the global properties of dynamical system, such as fractal basin boundaries. Firstly a rough cell structure is applied to the generalized cell mapping (GCM) method to obtain the general global properties of dynamical systems with digraph algorithm, and then a procedure based on the composite cell coordinate system method is proposed to increase the calculation accuracy. In order to further increase the calculation speed, a simple and feasible parallel strategy is applied during the creation process of one-step transition probability matrix for the GCM method. Meanwhile, the memory consumption can be greatly reduced by storing the one-step transition probability matrix as finite separate data files. The accurate global properties of two examples, a nonlinear oscillator with fractal basin structure and the Lorenz system, are demonstrated to show the effectiveness of our proposed improvement strategy.
AB - A modified procedure is proposed in this paper to solve the limitations of digraph cell mapping method in accurately analyzing the global properties of dynamical system, such as fractal basin boundaries. Firstly a rough cell structure is applied to the generalized cell mapping (GCM) method to obtain the general global properties of dynamical systems with digraph algorithm, and then a procedure based on the composite cell coordinate system method is proposed to increase the calculation accuracy. In order to further increase the calculation speed, a simple and feasible parallel strategy is applied during the creation process of one-step transition probability matrix for the GCM method. Meanwhile, the memory consumption can be greatly reduced by storing the one-step transition probability matrix as finite separate data files. The accurate global properties of two examples, a nonlinear oscillator with fractal basin structure and the Lorenz system, are demonstrated to show the effectiveness of our proposed improvement strategy.
KW - Composite cell coordinate system
KW - Fractal basin boundary
KW - Generalized cell mapping
KW - Global property
UR - http://www.scopus.com/inward/record.url?scp=85046154948&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2018.04.025
DO - 10.1016/j.chaos.2018.04.025
M3 - 文章
AN - SCOPUS:85046154948
SN - 0960-0779
VL - 111
SP - 206
EP - 212
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
ER -