On the computation of domains of attraction during the dynamic modelling of oscillating systems
type: Item
instance of: scholarly article
title: On the computation of domains of attraction during the dynamic modelling of oscillating systems
zbMATH Open document ID: 0657.70025
DOI: 10.1016/0307-904X(88)90088-1
author: L. N. Virgin
author: Dennis Leung
author: S. R. Bishop
published in: Applied Mathematical Modelling
publication date: 1988-01-01T00:00:00Z
review text: A particular feature of nonlinear differential equations is that they may have competing steady-state solutions. This paper describes some multiple dynamic responses typically found when modelling nonlinear systems with particular reference to the catchment regions which illustrate sensitivity to initial conditions. The form of dynamic behavior persisting after the decay of transient motion due to damping depends on the starting conditions in terms of initial displacement and velocity of the system. Methods of obtaining domains of attraction to particular stable solutions are described with reference to simple equations incorporating nonlinear resonance phenomena together with examples of coexisting subharmonic oscillations in offshore mechanics.
Mathematics Subject Classification ID: 70K30
zbMATH DE Number: 4074581
zbMATH Keywords: domains of attraction
zbMATH Keywords: subharmonic resonances
zbMATH Keywords: fractal basin boundaries
zbMATH Keywords: nonlinear dynamics
zbMATH Keywords: offshore mechanics
zbMATH Keywords: steady-state solutions
zbMATH Keywords: multiple dynamic responses
zbMATH Keywords: nonlinear systems
zbMATH Keywords: catchment regions
zbMATH Keywords: initial conditions
zbMATH Keywords: coexisting subharmonic oscillations
MaRDI profile type: Publication
cites work: Q3207313
cites work: Q3736576
cites work: Q3698356
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: A study of nonlinear periodic systems via the point mapping method
cites work: Q4744562
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full work available at URL: 0307-904x(88)90088-1
OpenAlex ID: W2106924561
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description: scientific article; zbMATH DE number 4074581