Stability Properties of Nonlinear Delay Systems and the Breakdown of the Adiabatic Approximation-Reference-Cited by-同舟云学术

Stability Properties of Nonlinear Delay Systems and the Breakdown of the Adiabatic Approximation

Published:1991-08-01 Issue:8 Volume:46 Page:686-690
ISSN:1865-7109
Container-title:Zeitschrift für Naturforschung A
language:en
Short-container-title:

Author:

Hawdon Brendan J.¹,O'Gorman James¹,Heffernan Daniel M.²

Affiliation:

1. Department of Pure and Applied Physics, Trinity College, Dublin 2, Ireland

2. School of Physical Sciences, Dublin City University, Dublin 9, Ireland and School of Theoretical Physics, Dublin Institute of Advanced Studies, Dublin 4, Ireland

Abstract

Abstract 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

Publisher

Walter de Gruyter GmbH

Subject

Physical and Theoretical Chemistry,General Physics and Astronomy,Mathematical Physics

Link

https://www.degruyter.com/document/doi/10.1515/zna-1991-0805/pdf

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1. Delay-induced instabilities in nonlinear feedback systems;Physical Review E;1994-01-01

2. Josephson junctions with delayed feedback;Physics Letters A;1992-12

3. Bifurcation structures into chaos of delay-differential equations for a passive optical ring resonator;Applied Physics B Photophysics and Laser Chemistry;1992-08