指数型一次Logistic迭代方程解的周期倍分岔现象

蔡惠京

数学学报 ›› 2001, Vol. 44 ›› Issue (4) : 761-768.

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PDF(382 KB)
数学学报 ›› 2001, Vol. 44 ›› Issue (4) : 761-768. DOI: 10.12386/A2001sxxb0098
论文

指数型一次Logistic迭代方程解的周期倍分岔现象

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

    Hui Jing CAI
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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.

Abstract

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

混沌 / 周期倍分岔 / Logistic迭代方程

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蔡惠京. 指数型一次Logistic迭代方程解的周期倍分岔现象. 数学学报, 2001, 44(4): 761-768 https://doi.org/10.12386/A2001sxxb0098
Hui Jing CAI. On the Period-Doubling Bifurcation of the Solutions of the First Order Exponential Logistic Iterative Equation. Acta Mathematica Sinica, Chinese Series, 2001, 44(4): 761-768 https://doi.org/10.12386/A2001sxxb0098
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