Strong delayed negative feedback - Erneux, Thomas (Frontiers in Network Physiology, 2024)
The new field of Network Physiology concentrates on coordinated network interactions among distinct organs in the human body. Mathematical models have benefited from the modeling on neuronal networks. We expect, however, stronger feedback interactions between human organs operating at different time scales. Delayed negative feedbacks slowing, stopping reactions, and generating oscillations could be essential for a stable synchronization of the network.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 nondelayed feedback functions and show that Hopf classical theory needs to be revisited in the strong feedback limit.