Title :
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
fDate :
7/1/2001 12:00:00 AM
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;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
