LOCAL BIFURCATIONS OF A QUASIPERIODIC ORBIT

被引：8

作者：

Banerjee, Soumitro ^{[1
,4
]}

Giaouris, Damian ^{[2
]}

Missailidis, Petros ^{[3
]}

Imrayed, Otman ^{[3
]}

机构：

[1] Indian Inst Sci Educ & Res Kolkata, Nadia 741252, WB, India

[2] Ctr Res & Technol Hellas CERTH, CPERI, Thermi 57001, Greece

[3] Newcastle Univ, Sch Elect Elect & Comp Engn, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England

[4] King Abdulaziz Univ, Jeddah 21413, Saudi Arabia

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2012年 / 22卷 / 12期

关键词：

Quasiperiodicity; bifurcation; torus; CONTROLLED DC/DC CONVERTERS; FAST-SCALE; DOUBLING BIFURCATIONS; VIBRATORY-SYSTEMS; TORUS; CONTINUATION; COMPUTATION; INSTABILITY; ATTRACTORS; CASCADE;

D O I：

10.1142/S0218127412502896

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the local bifurcations that can occur in a quasiperiodic orbit in a three-dimensional map: (a) a torus doubling resulting in two disjoint loops, (b) a torus doubling resulting in a single closed curve with two loops, (c) the appearance of a third frequency, and (d) the birth of a stable torus and an unstable torus. We analyze these bifurcations in terms of the stability of the point at which the closed invariant curve intersects a "second Poincare section". We show that these bifurcations can be classified depending on where the eigenvalues of this fixed point cross the unit circle.

引用

页数：12

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