Knipl, DH;
(2013)
Fundamental properties of differential equations with dynamically defined delayed feedback.
Electronic Journal of Qualitative Theory of Differential Equations
, 17
pp. 1-18.
10.14232/ejqtde.2013.1.17.
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Abstract
We consider an initial value problem for nonautonomous functional differential equations where the delay term is defined via the solution of another system of differential equations. We obtain the general existence and uniqueness result for the initial value problem by showing a Lipschitz property of the dynamically defined delayed feedback function and give conditions for the nonnegativity of solutions. We determine the steady-state solution of the autonomous system and obtain the linearized equation about the equilibria. Our work was motivated by biological applications where the model setup leads to a system of differential equations with such dynamically defined delay terms. We present a simple model from population dynamics with fixed period of temporary separation and an epidemic model with long distance travel and entry screening.
| Type: | Article |
|---|---|
| Title: | Fundamental properties of differential equations with dynamically defined delayed feedback |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.14232/ejqtde.2013.1.17 |
| Publisher version: | http://dx.doi.org/10.14232/ejqtde.2013.1.17 |
| Language: | English |
| Keywords: | functional differential equations, dynamically defined delay, Lipschitz property, biological applications |
| UCL classification: | UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1473755 |
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