Bifurcation analysis of delay-induced periodic oscillations

Bifurcation analysis of delay-induced periodic oscillations

Green, K.
TNO Bouw en Ondergrond

2010

In this paper we consider a generic differential equation with a cubic nonlinearity and delay. This system, in the absence of delay, is known to undergo an oscillatory instability. The addition of the delay is shown to result in the creation of a number of periodic solutions with constant amplitude and a constant frequency; the number of solutions increases with the size of the delay. Indeed, for many physical applications in which oscillatory instabilities are induced by a delayed response or feedback mechanism, the system under consideration forms the underlying backbone for a mathematical model. Our study showcases the effectiveness of performing a numerical bifurcation analysis, alongside the use of analytical and geometrical arguments, in investigating systems with delay. We identify curves of codimension-one bifurcations of periodic solutions. We show how these curves interact via codimension-two bifurcation points: double singularities which organise the bifurcations and dynamics in their local vicinity. © 2009 Elsevier B.V. All rights reserved.

Building Engineering & Civil Engineering
SD - Structural Dynamics
TS - Technical Sciences
Mechanics
Codimension-one and codimension-two bifurcations
Delay differential equations
Organising centres

http://resolver.tudelft.nl/uuid:19deeaf1-ed58-465f-8de6-63d32ee6739b

273916

0377-0427

Journal of Computational and Applied Mathematics, 233 (9), 2405-2412

article