TWO-PARAMETER STUDY OF TRANSITION TO CHAOS IN CHUA'S CIRCUIT: RENORMALIZATION GROUP, UNIVERSALITY AND SCALING

被引：23

作者：

Kuznetsov, A. P. ^{[1
]}

Kuznetsov, S. P. ^{[1
]}

Sataev, I. R. ^{[1
]}

Chua, L. O. ^{[2
]}

机构：

[1] Russian Acad Sci, Inst Radioengn & Elect, Zelenaja 38, Saratov 410019, Russia

[2] Univ Calif Berkeley, Dept Elect Engn & Comp Sci, Berkeley, CA 94720 USA

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 1993年 / 3卷 / 04期

关键词：

D O I：

10.1142/S0218127493000799

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A complex fine structure in the topography of regions of different dynamical behavior near the onset of chaos is investigated in a parameter plane of the 1D Chua's map, which describes approximately the dynamics of Chua's circuit. Besides piecewise-smooth Feigenbaum critical lines, the boundary of chaos contains an infinite set of codimension-2 critical points, which may be coded by itineraries on a binary tree. Renormalization group analysis is applied which is a generalization of Feigenbaum's theory for codimension-2 critical points. Multicolor high resolution maps of the parameter plane show that in regions near critical points having periodic codes, the infinitely intricate topography of the parameter plane reveals a property of self similarity.

引用

页码：943 / 962

页数：20