Bifurcation theory of a coupled system modelling the blood flow control in the kidney

Abstract

In this paper we present a bifurcation theory of a coupled system between a vector-valued transport equation and a system of differential equations with time delay, which finds many applications in biological systems. Via Lumer-Phillips' Theorem, we are able to prove the existence and uniqueness of a solution to such a system. Furthermore, we characterize the point spectrum of the operator associated with this system and a bifurcation analysis is performed. Finally, some numerical results applied to a model for the blood flow control in the kidney are presented.