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.
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收藏
页数：12
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