Please use this identifier to cite or link to this item:
http://hdl.handle.net/1983/472
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| Title: | Periodic solutions and their bifurcations in a non-smooth second-order delay differential equation |
| Author(s): | Barton, DAW
Krauskopf, B
Wilson, RE |
| Publication or creation date: | 2005 |
| 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. |
| Document type: | Preprint |
| Appears in Collections: | Bristol Centre for Applied Nonlinear Mathematics
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