Oscillations and Periodic Solutions in a Two-Dimensional Differential Delay Model

Anatoli F. Ivanov, Zari A. Dzalilov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A class of two-dimensional differential systems with delay and overall negative feedback is considered. Sufficient conditions for the existence of periodic solutions are established. The instability of the unique equilibrium together with the one-sided boundedness of one of the two nonlinearities lead to the existence of periodic solutions. Systems of this type appear in various applications in engineering and natural sciences, in particular in mathematical biology and physiology as models of circadian rhythm generator and glucose-insulin regulation models in humans.

Original languageEnglish (US)
Title of host publicationRecent Developments in Mathematical, Statistical and Computational Sciences - The V AMMCS International Conference, 2019
EditorsD. Marc Kilgour, Herb Kunze, Roman Makarov, Roderick Melnik, Xu Wang
PublisherSpringer
Pages59-70
Number of pages12
ISBN (Print)9783030635909
DOIs
StatePublished - 2021
EventInternational Conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2019 - Waterloo, Canada
Duration: Aug 18 2019Aug 23 2019

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume343
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2019
Country/TerritoryCanada
CityWaterloo
Period8/18/198/23/19

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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