动力学不连续性所导致的奇异排斥子

STRANGE REPELLER INDUCED BY DYNAMICAL DISCONTINUITY

借助一类具有“映孔”的分段线性一维映象，阐明“映孔导致激发”是“不连续性导致奇异排斥子”出现的结果．此奇异排斥子使得叠代轨道经过映孔逃出原混沌吸引子，从而造成混沌吸引子的突然扩张．证明了叠代轨道在原吸引子中的寿命反比于逃逸速率。

Abstract Employing a kind of piece wise linear map with a hole,we show that “hole induced crisis” is a result of the emergence of a “strange repeller due to discontinuity”. The strange repeller forces the iteration orbit to escape from the original chaotic attractor.Thus the attactor suddenly expands.We have proved that the lifetime of iterations in original attractor is inversely proportional to the escaping ratio,which enables us to obtain the dependence of the mean lifetime on the control parameter analytically.