Abstract By using the generalized cell mapping digraph (GCMD) method, we study bifurcations governing the escape of periodically forced oscillators in a potential well, in which a chaotic saddle plays an extremely important role. In this paper, we find the chaotic saddle, and we demonstrate that the chaotic saddle is embedded in a strange fractal boundary which has the Wada property, that any point on the boundary of that basin is also simultaneously on the boundary of at least two other basins. The chaotic saddle in the Wada fractal boundary, by colliding with a chaotic attractor, leads to a chaotic boundary crisis with a global indeterminate outcome which presents an extreme form of indeterminacy in a dynamical system. We also investigate the origin and evolution of the chaotic saddle in the Wada fractal boundary, particularly concentrating on its discontinuous bifurcations (metamorphoses). We demonstrate that the chaotic saddle in the Wada fractal boundary is created by the collision between two chaotic saddles in different fractal boundaries. After a final escape bifurcation, there only exists the attractor at infinity; a chaotic saddle with a beautiful pattern is left behind in phase space.
Received: 30 December 2001
Revised: 26 April 2002
Accepted manuscript online:
PACS:
05.45.Df
(Fractals)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 10172067 and 19972051).
Cite this article:
Hong Ling (洪灵), Xu Jian-Xue (徐健学) Study of the Wada fractal boundary and indeterminate crisis 2002 Chinese Physics 11 1115
GLOBAL ANALYSIS OF SPECTRA OF THE PO2 RADICAL IN THE GAS PHASE Liu Yu-yan (刘煜炎), Liu Xiao-yong (刘效庸), Liu Hong-ping (刘红平), Guo Yuan-qing (郭远清), Huang Guang-ming (黄光明), Lin Jie-li (林洁丽), Gao Hui (高晖), Duan Chuan-xi (段传喜). Chin. Phys. B, 2000, 9(9): 652-655.
No Suggested Reading articles found!
Viewed
Full text
Abstract
Cited
Altmetric
blogs
tweeters
Facebook pages
Wikipedia page
Google+ users
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
