STABILITY PROPERTIES OF NONLINEAR DELAY SYSTEMS AND THE BREAKDOWN OF THE ADIABATIC APPROXIMATION

被引：2

作者：

HAWDON, BJ

OGORMAN, J

HEFFERNAN, DM

机构：

[1] DUBLIN CITY UNIV,SCH PHYS SCI,DUBLIN 9,IRELAND

[2] UNIV DUBLIN TRINITY COLL,DEPT PURE & APPL PHYS,DUBLIN 2,IRELAND

[3] DUBLIN INST ADV STUDIES,SCH THEORET PHYS,DUBLIN 4,IRELAND

来源：

ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES | 1991年 / 46卷 / 08期

关键词：

STABILITY; CHAOS; ADIABATIC APPROXIMATION;

D O I：

10.1515/zna-1991-0805

中图分类号：

O64 [物理化学（理论化学）、化学物理学];

学科分类号：

070304 ; 081704 ;

摘要：

We consider the adiabatic approximation as it is applied to a familiar class of infinite-dimensional equations. We show how this approximation may be directly invalidated by analyzing a statistical form of the eigenvalue equation before and after the adiabatic approximation is made. We introduce a statistical quantity which can be used to predict the existence of periodic windows in the chaotic regime.

引用

页码：686 / 690

页数：5

共 13 条

[1]

FARMER JD, 1982, PHYSICA D, V4, P366, DOI 10.1016/0167-2789(82)90042-2

[2]

HAKEN H, 1986, OPTICAL INSTABILITIE

[3] DYNAMICAL STUDIES OF A HYBRID OPTICAL BISTABLE SYSTEM [J].

HAWDON, BJ ;

OGORMAN, J ;

HEFFERNAN, DM .

JOURNAL DE PHYSIQUE, 1988, 49 (C-2) :419-422

[4] CHARACTERIZATION OF CHAOS IN A HYBRID OPTICALLY BISTABLE DEVICE [J].

HOPF, FA ;

KAPLAN, DL ;

ROSE, MH ;

SANDERS, LD ;

DERSTINE, MW .

PHYSICAL REVIEW LETTERS, 1986, 57 (12) :1394-1397

[5] SUCCESSIVE HIGHER-HARMONIC BIFURCATIONS IN SYSTEMS WITH DELAYED FEEDBACK [J].

IKEDA, K ;

KONDO, K ;

AKIMOTO, O .

PHYSICAL REVIEW LETTERS, 1982, 49 (20) :1467-1470

[6]

IKEDA K, 1986, OPTICAL INSTABILITIE

[7]

Kaplan J. L., 1979, FUNCTIONAL DIFFERENT, V730, P204, DOI DOI 10.1007/BFB0064319

[8] HIGH-DIMENSION CHAOTIC ATTRACTORS OF A NONLINEAR RING CAVITY [J].

LEBERRE, M ;

RESSAYRE, E ;

TALLET, A ;

GIBBS, HM .

PHYSICAL REVIEW LETTERS, 1986, 56 (04) :274-277

[9]

MILONNI PW, 1987, CHAOS LASER MATTER

[10] FEEDBACK INDUCED INSTABILITIES IN EXTERNAL CAVITY INJECTION-LASERS [J].

OGORMAN, J ;

HAWDON, BJ ;

HEGARTY, J ;

HEFFERNAN, DM .

ELECTRONICS LETTERS, 1989, 25 (02) :114-115

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