Chaotic characteristics of a one-dimensional iterative map with infinite collapses

Author

He, Di ; He, Chen ; Jiang, Ling-ge ; Zhu, Hong-wen ; Hu, Guang-rui

Author_Institution

Dept. of Electron. Eng., Shanghai Jiaotong Univ., China

Volume

48

Issue

7

fYear

2001

fDate

7/1/2001 12:00:00 AM

Firstpage

900

Lastpage

906

Abstract

A one-dimensional iterative chaotic map with infinite collapses within symmetrical region [-1, O)∪(O, +1] is proposed. The stability of fixed points and that around the singular point are analyzed. Higher Lyapunov exponents of proposed map show stronger chaotic characteristics than some iterative and continuous chaotic models usually used. There exist inverse bifurcation phenomena and special main periodic windows at certain positions shown in the bifurcation diagram, which can explain the generation mechanism of chaos. The chaotic model with good properties can be generated if choosing the parameter of the map properly. Stronger inner pseudorandom characteristics can also be observed through χ² test on the supposition of even distribution. This chaotic model may have many advantages in practical use

Keywords

Lyapunov methods; bifurcation; chaos; iterative methods; nonlinear dynamical systems; poles and zeros; Lyapunov exponents; bifurcation diagram; chaotic characteristics; fixed points; generation mechanism; infinite collapses; inner pseudorandom characteristics; inverse bifurcation phenomena; one-dimensional iterative map; singular point; symmetrical region; Chaos; Circuits; Polynomials;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.933333

Filename

933333