BIFURCATIONS OF SNAP-BACK REPELLERS WITH APPLICATION TO BORDER-COLLISION BIFURCATIONS

被引：7

作者：

Glendinning, Paul ^{[1
,2
]}

机构：

[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

[2] Univ Manchester, CICADA, Manchester M13 9PL, Lancs, England

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2010年 / 20卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

Snap-back-repeller; hybrid system; border-collision bifurcation; IMPLY CHAOS; SYSTEMS;

D O I：

10.1142/S0218127410025557

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The bifurcation theory of snap-back repellers in hybrid dynamical systems is developed. Infinite sequences of bifurcations are shown to arise due to the creation of snap-back repellers in noninvertible maps. These are analogous to the cascades of bifurcations known to occur close to homoclinic tangencies for diffeomorphisms. The theoretical results are illustrated with reference to bifurcations in the normal form for border-collision bifurcations.

引用

页码：479 / 489

页数：11

共 15 条

[1]

[Anonymous], 1972, Mathematics of the USSR-Sbornik

[2] Border collision bifurcations in two-dimensional piecewise smooth maps [J].

Banerjee, S ;

Grebogi, C .

PHYSICAL REVIEW E, 1999, 59 (04) :4052-4061

[3] Robust chaos [J].

Banerjee, S ;

Yorke, JA ;

Grebogi, C .

PHYSICAL REVIEW LETTERS, 1998, 80 (14) :3049-3052

[4] Snap-back repellers and scrambled sets in general topological spaces [J].

Boyarsky, A ;

Góra, P ;

Lioubimov, V .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 43 (05) :591-604

[5] HOMOCLINIC ORBITS AND MIXED-MODE OSCILLATIONS IN FAR-FROM-EQUILIBRIUM SYSTEMS [J].

GASPARD, P ;

WANG, XJ .

JOURNAL OF STATISTICAL PHYSICS, 1987, 48 (1-2) :151-199

[6]

Gavrilov N. K., 1973, Math. USSR-Sb, V19, P139, DOI [10.1070%2Fsm1973v019n01abeh001741, 10.1070/SM1973v019n01ABEH001741, DOI 10.1070/SM1973V019N01ABEH001741]

[7] Border collision bifurcations, snap-back repellers, and chaos [J].

Glendinning, Paul ;

Wong, Chi Hong .

PHYSICAL REVIEW E, 2009, 79 (02)

[8]

Guckenheimer J., 2013, NONLINEAR OSCILLATIO, V42

[9] An improved version of the Marotto theorem [J].

Li, CP ;

Chen, GR .

CHAOS SOLITONS & FRACTALS, 2003, 18 (01) :69-77

[10]

Lin W, 2007, DISCRETE CONT DYN-A, V19, P103

← 1 2 →