Homoclinic bifurcations in Chua's circuit

被引:18
作者
Kahan, S [1 ]
Sicardi-Schifino, AC [1 ]
机构
[1] Univ Republ, Inst Fis, Montevideo 11000, Uruguay
来源
PHYSICA A | 1999年 / 262卷 / 1-2期
关键词
homoclinic; bifurcation; electronic; circuit;
D O I
10.1016/S0378-4371(98)00389-6
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In this paper we study the possible relationship between the Birth of the Double Scroll [L.O. Chua et al., IEEE-CAS 33 (11) (1986) 1073] and the homoclinic bifurcations in the: traditional Chua's equations. Using a one-dimensional Poincare map we determine the existence of secondary symmetric homoclinic orbits of Shil'nikov type, born with the Chua's attractor, connecting unstable and stable manifolds of the trivial equilibrium point. In addition, taking into account the presence of other homoclinic orbits for the asymmetric attractor and heteroclinic orbits for the symmetric attractor (connecting unstable and stable manifold of the non-trivial equilibrium points), we suggest a hypothesis about the Birth of Double Scroll structure on the (alpha, beta) plane. (C) 1999 Published by Elsevier Science B.V. All rights reserved.
引用
收藏
页码:144 / 152
页数:9
相关论文
共 14 条
[1]  
[Anonymous], IEEE T CAS
[2]  
[Anonymous], 1979, ANN NY ACAD SCI
[3]   AN IC CHIP OF CHUA CIRCUIT [J].
CRUZ, JM ;
CHUA, LO .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-ANALOG AND DIGITAL SIGNAL PROCESSING, 1993, 40 (10) :614-625
[4]   CHAOS SHIFT KEYING - MODULATION AND DEMODULATION OF A CHAOTIC CARRIER USING SELF-SYNCHRONIZING CHUA CIRCUITS [J].
DEDIEU, H ;
KENNEDY, MP ;
HASLER, M .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-ANALOG AND DIGITAL SIGNAL PROCESSING, 1993, 40 (10) :634-642
[5]   A CASE-STUDY FOR HOMOCLINIC CHAOS IN AN AUTONOMOUS ELECTRONIC-CIRCUIT - A TRIP FROM TAKENS-BOGDANOV TO HOPF-SILNIKOV [J].
FREIRE, E ;
RODRIGUEZLUIS, AJ ;
GAMERO, E ;
PONCE, E .
PHYSICA D-NONLINEAR PHENOMENA, 1993, 62 (1-4) :230-253
[6]   BIFURCATION PHENOMENA NEAR HOMOCLINIC SYSTEMS - A 2-PARAMETER ANALYSIS [J].
GASPARD, P ;
KAPRAL, R ;
NICOLIS, G .
JOURNAL OF STATISTICAL PHYSICS, 1984, 35 (5-6) :697-727
[7]   WHAT CAN WE LEARN FROM HOMOCLINIC ORBITS IN CHAOTIC DYNAMICS [J].
GASPARD, P ;
NICOLIS, G .
JOURNAL OF STATISTICAL PHYSICS, 1983, 31 (03) :499-518
[8]   LOCAL AND GLOBAL BEHAVIOR NEAR HOMOCLINIC ORBITS [J].
GLENDINNING, P ;
SPARROW, C .
JOURNAL OF STATISTICAL PHYSICS, 1984, 35 (5-6) :645-696
[9]   ON PERIODIC ORBITS AND HOMOCLINIC BIFURCATIONS IN CHUA'S CIRCUIT WITH A SMOOTH NONLINEARITY [J].
Khibnik, Alexander I. ;
Roose, Dirk ;
Chua, Leon O. .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1993, 3 (02) :363-384
[10]  
KOCAREV L, 1992, INT J BIFURCAT CHAOS, V2, P705