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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Description/Abstract
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
| Item Type: | Article |
|---|---|
| ISSNs: | 1468-9367 (print) 1468-9375 (electronic) |
| Subjects: | T Technology > TA Engineering (General). Civil engineering (General) |
| Divisions: | University Structure - Pre August 2011 > School of Civil Engineering and the Environment |
| Item ID: | 184259 |
| 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) |
| Date: | 2006 |
| Status: | Published |
| URI: | http://eprints.soton.ac.uk/id/eprint/184259 |
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