Oscillations in Low-Dimensional Cyclic Differential Delay Systems

Anatoli F. Ivanov, Zari A. Dzalilov

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

Abstract

Nonlinear autonomous N-dimensional systems of cyclic differential equations with delays and overall negative feedback are considered. Such systems serve as mathematical models of numerous real world phenomena in physics and laser optics, physiology and mathematical biology, economics and life sciences among others. In the case of lower dimensions and sufficient conditions are derived for the oscillation of all solutions about the unique equilibrium. Open problems and conjectures are discussed for the higher dimensional case and for more convoluted sign feedbacks.

Original languageEnglish (US)
Title of host publicationRecent Advances in Mathematical and Statistical Methods - IV AMMCS International Conference
EditorsHerb Kunze, D. Marc Kilgour, Roman Makarov, Roderick Melnik, Xu Wang
PublisherSpringer New York LLC
Pages603-613
Number of pages11
ISBN (Print)9783319997186
DOIs
Publication statusPublished - Jan 1 2018
EventInternational conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2017 - Waterloo, Canada
Duration: Aug 20 2017Aug 25 2017

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume259
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

OtherInternational conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2017
CountryCanada
CityWaterloo
Period8/20/178/25/17

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Ivanov, A. F., & Dzalilov, Z. A. (2018). Oscillations in Low-Dimensional Cyclic Differential Delay Systems. In H. Kunze, D. M. Kilgour, R. Makarov, R. Melnik, & X. Wang (Eds.), Recent Advances in Mathematical and Statistical Methods - IV AMMCS International Conference (pp. 603-613). (Springer Proceedings in Mathematics and Statistics; Vol. 259). Springer New York LLC. https://doi.org/10.1007/978-3-319-99719-3_54