An impulsive model of endocrine regulation with two negative feedback loops

Hadi Taghvafard, Anton V. Proskurnikov, Ming Cao

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

4 Citations (Scopus)
18 Downloads (Pure)


Whereas obtaining a global model of the human endocrine system remains a challenging problem, visible progress has been demonstrated in modeling its subsystems (axes) that regulate production of specific hormones. The axes are typically described by Goodwin-like cyclic feedback systems. Unlike the classical Goodwin oscillator, obeying a system of ordinary differential equations, the feedback mechanisms of brain-controlled hormonal regulatory circuits appear to be pulsatile, which, in particular, exclude the possibility of equilibrium solutions. The recent studies have also revealed that the regulatory mechanisms of many vital hormones (including e.g. testosterone and cortisol regulation) are more complicated than Goodwin-type oscillators and involve multiple negative feedback loops. Although a few “multi-loop” extensions of the classical Goodwin model have been studied in literature, the analysis of impulsive endocrine regulation models with additional negative feedbacks has remained elusive. In this paper, we address one of such models, obtained from the impulsive Goodwin-type oscillator by introducing an additional linear feedback. Since the levels of hormones’ concentrations oscillate periodically, examination of endocrine regulation circuits is primarily focused on periodic solutions. We prove the existence and uniqueness of periodic solutions of a special type, referred to as 1-cycles and featured by the unique discontinuous point in each period. Procedures for computing such a solution and testing its stability are discussed. The results are confirmed by numerical simulations.

Original languageEnglish
Title of host publicationIFAC-PapersOnLine
Subtitle of host publicationProceedings of the 20th IFAC World Congress
EditorsDenis Dochain, Didier Henrion, Dimitri Peaucelle
Place of PublicationLaxenburg, Austria
Publication statusPublished - 2017
Event20th World Congress of the International Federation of Automatic Control (IFAC), 2017 - Toulouse, France
Duration: 9 Jul 201714 Jul 2017
Conference number: 20

Publication series

ISSN (Print)2405-8963


Conference20th World Congress of the International Federation of Automatic Control (IFAC), 2017
Abbreviated titleIFAC 2017
Internet address


  • Biomedical systems
  • Impulse signals
  • Oscillations
  • Periodic solutions


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