On global properties of time-delayed feedback control: weakly nonlinear analysis

被引：22
作者：
Just, W
Benner, H
von Loewenich, C
机构：
[1] Univ London Queen Mary Coll, Sch Math Sci, London E1 4NS, England
[2] TH Darmstadt, Inst Solid State Phys, D-64289 Darmstadt, Germany
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2004年 / 199卷 / 1-2期
关键词：
control of chaos; differential-difference equations; codimension two bifurcations; hysteresis;
D O I：
10.1016/j.physd.2004.08.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We address the problem which type of initial state yields successful stabilisation when time-delayed feedback control is applied. Using well known concepts from bifurcation theory we provide a general mechanism that limits the corresponding basins of attraction. Application of normal form analysis to general delay-differential equations proves the universality of our results. The empirical criteria which determine the prospective size of the basin are easily accessible and a demonstration in terms of a simple numerical simulation is provided. (C) 2004 Elsevier B.V. All rights reserved.
引用
收藏
页码：33 / 44
页数：12
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