Local and global analysis of endocrine regulation as a non-cyclic feedback system

Taghvafard, Hadi; Proskurnikov, A.V.; Cao, Ming

doi:10.1016/j.automatica.2018.01.035

Local and global analysis of endocrine regulation as a non-cyclic feedback system

Title

Local and global analysis of endocrine regulation as a non-cyclic feedback system

Author

Taghvafard, Hadi (University Medical Center Groningen)
Proskurnikov, A.V. (TU Delft Team Tamas Keviczky; ITMO University; Russian Academy of Sciences)
Cao, Ming (University Medical Center Groningen)

Date

2018

Abstract

To understand the sophisticated control mechanisms of the human's endocrine system is a challenging task that is a crucial step towards precise medical treatment of many dysfunctions and diseases. Although mathematical models describing the endocrine system as a whole are still elusive, recently some substantial progress has been made in analyzing theoretically its subsystems (or axes) that regulate the production of specific hormones. Secretion of many vital hormones, responsible for growth, reproduction and metabolism, is orchestrated by feedback mechanisms that are similar in structure to the model of simple genetic oscillators, proposed first by B.C. Goodwin. Unlike the celebrated Goodwin's model, the endocrine regulation mechanisms are in fact known to have non-cyclic structures and involve multiple feedbacks; a Goodwin-type model thus represents only a part of such a complicated mechanism. In this paper, we examine a non-cyclic feedback system of hormonal regulation, obtained from the classical Goodwin's oscillator by introducing an additional negative feedback. We establish global properties of this model and show, in particular, that the local instability of its unique equilibrium implies that almost all system's solutions oscillate; furthermore, under additional restrictions these solutions converge to periodic or homoclinic orbits.

Subject

Biomedical systems
Oscillations
Periodic solutions
Stability

To reference this document use:

http://resolver.tudelft.nl/uuid:259ac0ad-594a-4800-bd80-16f8f35897b7

DOI

https://doi.org/10.1016/j.automatica.2018.01.035

Embargo date

2020-03-20

ISSN

0005-1098

Source

Automatica, 91, 190-196