Hidden attractor in smooth Chua systems

被引：463
作者：
Leonov, G. A. [2 ,3 ]
Kuznetsov, N. V. [1 ,2 ]
Vagaitsev, V. I. [1 ,2 ]
机构：
[1] Univ Jyvaskyla, Dept Math Informat Technol, FIN-40014 Agora, Finland
[2] St Petersburg State Univ, Appl Cybernet Dept, St Petersburg 198504, Russia
[3] Harbin Inst Technol, Harbin 150001, Peoples R China
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2012年 / 241卷 / 18期
基金：
芬兰科学院; 俄罗斯基础研究基金会;
关键词：
Hidden oscillation; Attractor localization; Hidden attractor; Smooth Chua's system; HARMONIC LINEARIZATION; OSCILLATIONS; ALGORITHMS; CIRCUITS; AIZERMAN; CHAOS;
D O I：
10.1016/j.physd.2012.05.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The hidden oscillations (a basin of attraction of which does not contain neighborhoods of equilibria) have been obtained first in the 50-60s of the 20th century in automatic control systems with scalar piecewise-linear nonlinearity. This brings up the question about the excitation nature of hidden oscillations. In the present paper it is shown that hidden oscillations can exist not only in systems with piecewise-linear nonlinearity but also in smooth systems. Here the possibility of the existence of a hidden chaotic attractor in a modified Chua's system with a smooth characteristic of nonlinear element is demonstrated. (C) 2012 Elsevier B.V. All rights reserved.
引用
收藏
页码：1482 / 1486
页数：5
相关论文
共 35 条
[1]  
Aizerman M.A., 1949, RUSS MATH SURV, V4, P186
[2]   Theoretical and experimental time series analysis of an inductorless Chua's circuit [J].
Albuquerque, Holokx A. ;
Rubinger, Rero M. ;
Rech, Paulo C. .
PHYSICA D-NONLINEAR PHENOMENA, 2007, 233 (01) :66-72
[3]  
[Anonymous], 1918, ERZWUNGENE SCHWINGUN
[4]  
Arnold V. I., 2005, Experimental Mathematics
[5]  
Belousov B.P., 1951, Oscillation and Travelling Waves in Chemical Systems
[6]  
Bernat J., 1996, DYN CONTIN DISCRET I, V2, P337
[7]  
Bilotta E., 2008, WORLD SCI SER NONL A, V61
[8]   Algorithms for Finding Hidden Oscillations in Nonlinear Systems. The Aizerman and Kalman Conjectures and Chua's Circuits [J].
Bragin, V. O. ;
Vagaitsev, V. I. ;
Kuznetsov, N. V. ;
Leonov, G. A. .
JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL, 2011, 50 (04) :511-543
[9]   A GLIMPSE OF NONLINEAR PHENOMENA FROM CHUAS OSCILLATOR [J].
CHUA, LO .
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1995, 353 (1701) :3-12
[10]   CANONICAL REALIZATION OF CHUA CIRCUIT FAMILY [J].
CHUA, LO ;
LIN, GN .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1990, 37 (07) :885-902
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