ISSN:
1573-269X
Keywords:
Global analysis
;
cell references
;
the attracting sets
;
fractal basin boundary
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In iterative method of Point Mapping under Cell Reference, a cell co-ordinate system, called cell reference, is built to identify the subregions (cells) in the state space. When the cell reference is equipped with the so-called characteristic functions, it can work as an ‘inspector’ or a ‘recorder’ to derive the local dynamics of the subregions from the information provided by the trajectories passing through them. This method can retain the accuracy of the Point Mapping Method but greatly reduce the computational work. In this paper, the theoretic basis for this method is first discussed and a multiscale reference technique is then devised which can select an optimal cell reference and make the method more practicable. Finally, an example for application is presented. It is shown that the present method cannot only accurately and efficiently depict the basins of attraction of a dynamical system but also potentially detect other characteristics of the system.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008216629740
Permalink
