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

2020/07/17 by Serge Nicaise, Nicaise, Serge, Alessandro Paolucci +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Numerical methods for differential equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2007.09014

openalex publication_date 2020/07/17 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

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

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