Determining the Stability Domain of Perturbed Four-Dimensional Systems in 1:1 Resonance

Hoveijn, Igor and Kirillov, Oleg (2014) Determining the Stability Domain of Perturbed Four-Dimensional Systems in 1:1 Resonance. In: Nonlinear Physical Systems. Wiley, London, pp. 155-175. ISBN 9781848214200

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Official URL: http://dx.doi.org/10.1002/9781118577608.ch8

Abstract

In an analogy with the problems of non-Hermitian physics, nilpotent 1:1 resonances can originate in the unfolding of the 1:1 semi-simple resonance. This chapter presents a detailed study of this process in the case of general four-dimensional systems. It indicates how the results can be applied to an explicitly given system. The following questions are addressed: Determine the stability domain in parameter space of the original system; Locate the singularities on the boundary of the stability domain; and Identify Hamiltonian and reversible subsystems. The authors find the boundary of the stability domain and list all its singularities including six self-intersections and four “Whitney umbrellas”. They propose an algorithm of approximation of the stability boundary near singularities and apply the results to the study of enhancement of the modulation instability with dissipation as well as to the study of stability of a non-conservative system of rotor dynamics.

Item Type: Book Section
Uncontrolled Keywords: four-dimensional systems, Hamiltonian systems, modulation instability; non-Hermitian physics, resonance rotor dynamics; stability domain, Whitney umbrellas
Subjects: F300 Physics
G100 Mathematics
H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Oleg Kirillov
Date Deposited: 06 Feb 2017 11:21
Last Modified: 06 Feb 2017 11:21
URI: http://nrl.northumbria.ac.uk/id/eprint/29489

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