Periodic solutions and their bifurcations in a non-smooth second-order delay differential equation
Barton, DAW, Krauskopf, B and Wilson, R. Eddie (2006) Periodic solutions and their bifurcations in a non-smooth second-order delay differential equation. Dynamical Systems, 21, (3), 289-311. (doi:10.1080/14689360500539363).
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We consider a non-smooth second order delay differential equation (DDE) that was previously studied as a model of the pupil light reflex. It can also be viewed as a prototype model for a system operated under delayed relay control. We use the explicit construction of solutions of the non-smooth DDE hand-in-hand with a numerical continuation study of a related smoothed system. This allows us to produce a comprehensive global picture of the dynamics and bifurcations, which extends and completes previous results. Specifically, we find a rich combinatorial structure consisting of solution branches connected at resonance points. All new solutions of the smoothed system were subsequently constructed as solutions of the non-smooth system. Furthermore, we show an example of the unfolding in the smoothed system of a non-smooth bifurcation point, from which infinitely many solution branches emanate. This shows that smoothing of the DDE may provide insight even into bifurcations that can only occur in non-smooth systems
|Subjects:||T Technology > TA Engineering (General). Civil engineering (General)|
|Divisions:||University Structure - Pre August 2011 > School of Civil Engineering and the Environment
|Date Deposited:||12 May 2011 11:47|
|Last Modified:||20 Jul 2012 03:38|
|Contributors:||Barton, DAW (Author)
Krauskopf, B (Author)
Wilson, R. Eddie (Author)
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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