Abstract A chaotic synchronized system of two coupled skew tent maps is discussed in this paper. The locally and globally riddled basins of the chaotic synchronized attractor are studied. It is found that there is a novel phenomenon in the local－global riddling bifurcation of the attractive basin of the chaotic synchronized attractor in some specific coupling intervals. The coupling parameter corresponding to the locally riddled basin has a single value which is embedded in the coupling parameter interval corresponding to the globally riddled basin, just like a breakpoint. Also, there is no relation between this phenomenon and the form of the chaotic synchronized attractor. This phenomenon is found analytically. We also try to explain it in a physical sense. It may be that the chaotic synchronized attractor is in the critical state, as it is infinitely close to the boundary of its attractive basin. We conjecture that this isolated critical value phenomenon will be common in a system with a chaotic attractor in the critical state, in spite of the system being discrete or differential.
Received: 17 November 2001
Revised: 27 December 2001
Accepted manuscript online:
Fund: Project supported by the key project of the National Natural Science Foundation of China (Grant No 30030040).
Cite this article:
Tan Ning (谭宁), Xu Jian-Xue (徐健学), Chen Yong-Hong (陈永红) The isolated critical value phenomenon in local－global riddling bifurcation 2002 Chinese Physics 11 670
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