AUTHOR=Erneux Thomas 

TITLE=Strong delayed negative feedback

JOURNAL=Frontiers in Network Physiology

VOLUME=4

YEAR=2024

URL=https://www.frontiersin.org/journals/network-physiology/articles/10.3389/fnetp.2024.1399272

DOI=10.3389/fnetp.2024.1399272

ISSN=2674-0109

ABSTRACT=<p>In this paper, we analyze the strong feedback limit of two negative feedback schemes which have proven to be efficient for many biological processes (protein synthesis, immune responses, breathing disorders). In this limit, the nonlinear delayed feedback function can be reduced to a function with a threshold nonlinearity. This will considerably help analytical and numerical studies of networks exhibiting different topologies. Mathematically, we compare the bifurcation diagrams for both the delayed and non-delayed feedback functions and show that Hopf classical theory needs to be revisited in the strong feedback limit.</p>