In a two-dimensional area-preserving map we found a kind of noninvertibility that is induced by a piece-wise smooth property of the map.This can lead to the appearance of such kinds of elliptic islands that attract th...In a two-dimensional area-preserving map we found a kind of noninvertibility that is induced by a piece-wise smooth property of the map.This can lead to the appearance of such kinds of elliptic islands that attract the iterations from a set of initial values outside themselves,while behaving regularly inside.We suggest calling such islands quasi-attractors.展开更多
A kind of crisis with special scaling properties has been observed in a discontinuous map.The crisis happens via a collision between a discontinuity of the mapping function and an unstable periodic orbit locating on t...A kind of crisis with special scaling properties has been observed in a discontinuous map.The crisis happens via a collision between a discontinuity of the mapping function and an unstable periodic orbit locating on the basin boundary of the chaotic attractor.The scaling property of the crisis is<τ>∝∈-1.8,where<τ>and∈stand for the average characteristic time and the control parameter value crossing the critical point,respectively.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.19975039,49474216 and 59876093the Natural Science Foundation of Jiangsu Provincial Education Committee under Grant No.98kjb140006the Chinese National Basic Research Climbing Project.
文摘In a two-dimensional area-preserving map we found a kind of noninvertibility that is induced by a piece-wise smooth property of the map.This can lead to the appearance of such kinds of elliptic islands that attract the iterations from a set of initial values outside themselves,while behaving regularly inside.We suggest calling such islands quasi-attractors.
基金Supported by the National Natural Science Foundation of China under Grant No.19575037。
文摘A kind of crisis with special scaling properties has been observed in a discontinuous map.The crisis happens via a collision between a discontinuity of the mapping function and an unstable periodic orbit locating on the basin boundary of the chaotic attractor.The scaling property of the crisis is<τ>∝∈-1.8,where<τ>and∈stand for the average characteristic time and the control parameter value crossing the critical point,respectively.
