指数型一次Logistic迭代方程解的周期倍分岔现象  

On the Period-Doubling Bifurcation of the Solutions of the First Order Exponential Logistic Iterative Equation

作　　者：蔡惠京[1] 

机构地区：[1]广东中山学院,广东中山528402

出　　处：《数学学报（中文版）》2001年第4期761-768,共8页Acta Mathematica Sinica：Chinese Series

摘　　要：本文讨论了指数型一次Ｌｏｇｉｓｔｉｃ迭代方程解的周期倍分岔现象的存在性，给出了周期倍分合时的临界点参数应满足的方程，并证明了周期倍分岔的临界点参数序列的极限是存在的，进而证明了当参数越过这个极限时，指数型一次 Ｌｏｇｉｓｔｉｃ迭代方程存在混沌解．In this paper, it is proved that the period-doubling bifurcation of the solutions of the first order exponential Logistic iterative equation is existent. The equation that must be satisfied by critical bifurcation parameters is given. And it is showed that the critical bifurcation parameter sequence has a limit. Then, it is proved that the first order exponential Logistic iterative equation has a chaotic solution when the parameter is over the limit.

关 键 词：Logistic迭代方程 周期倍分岔 混沌 指数型 参数序列 极限 

分 类 号：O177.91[理学—数学]