Fundamental properties of differential equations with dynamically defined delayed feedback

Diana Knipl
2013 Electronic Journal of Qualitative Theory of Differential Equations  
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
more » ... in 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.
doi:10.14232/ejqtde.2013.1.17 fatcat:ute6up3uifcu5nn3vjjkustexu