@inproceedings{3a45f5493711418bb0d45f6723c7643b,
title = "Oscillations and Periodic Solutions in a Two-Dimensional Differential Delay Model",
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.",
author = "Ivanov, {Anatoli F.} and Dzalilov, {Zari A.}",
note = "Funding Information: Acknowledgements This work was initiated in the fall 2016 during A. Ivanov{\textquoteright}s visit and research stay at the University of Giessen, Germany, under the support of the Alexander von Humboldt Stiftung. In its final stages and during the preparation for publication A. Ivanov and Z. Dzalilov were supported by internal grants from the Federation University Australia (Ballarat, Victoria). Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.; International Conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2019 ; Conference date: 18-08-2019 Through 23-08-2019",
year = "2021",
doi = "10.1007/978-3-030-63591-6_6",
language = "English (US)",
isbn = "9783030635909",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer",
pages = "59--70",
editor = "Kilgour, {D. Marc} and Herb Kunze and Roman Makarov and Roderick Melnik and Xu Wang",
booktitle = "Recent Developments in Mathematical, Statistical and Computational Sciences - The V AMMCS International Conference, 2019",
}