Bifurcation analysis of a coupled system between a transport equation and an ordinary differential equation with time delay

TL;DR

This paper conducts a spectral and bifurcation analysis of a coupled transport-ODE system with delay, revealing stability regions, bifurcation points, and oscillatory behaviors relevant to kidney blood flow modeling.

Contribution

It provides the first detailed spectral and bifurcation analysis of a coupled transport-ODE system with delay, applied to kidney blood flow control.

Findings

Identified stability regions in parameter space.

Characterized bifurcation points leading to oscillations.

Numerical examples confirm theoretical predictions.

Abstract

In this paper we analyze a coupled system between a transport equation and an ordinary differential equation with time delay (which is a simplified version of a model for kidney blood flow control). Through a careful spectral analysis we characterize the region of stability, namely the set of parameters for which the system is exponentially stable. Also, we perform a bifurcation analysis and determine some properties of the stable steady state set and the limit cycle oscillation region. Some numerical examples illustrate the theoretical results.