@article{2a286df3c01d4398b55fb9a6113a950e,
title = "A cyclic system with delay and its characteristic equation",
abstract = "A nonlinear cyclic system with delay and the overall negative feedback is considered. The characteristic equation of the linearized system is studied in detail. Sufficient conditions for the oscillation of all solutions and for the existence of monotone solutions are derived in terms of roots of the characteristic equation.",
author = "Elena Braverman and Karel Hasik and Ivanov, {Anatoli F.} and Trofimchuk, {Sergei I.}",
note = "Funding Information: Hence, the Banach contraction principle guarantees the existence of the required solution z∗ ∈ B. □ Acknowledgments. This research project was initiated in July 2016 during the BIRS Workshop “Research in Teams”, 16RiT675 (BIRS, Banff, AB, Canada). The authors are grateful to the BIRS for providing the excellent collaborative environment and comprehensive support for our group. E. Braverman was partially supported by the NSERC research grant RGPIN-2015-05976. In the follow up work on this paper, A. Ivanov was partially supported by the Alexander von Humboldt Stiftung (Germany). S. Trofimchuk gratefully acknowledges the support of FONDECYT (Chile), project 1150480 as well as the NSERC research grant RGPIN-2015-05976 for partial support of travel expenses. Funding Information: This research project was initiated in July 2016 during the BIRS Workshop ?Research in Teams?, 16RiT675 (BIRS, Banff, AB, Canada). The authors are grateful to the BIRS for providing the excellent collaborative environment and comprehensive support for our group. E. Braverman was partially supported by the NSERC research grant RGPIN-2015-05976. In the follow up work on this paper, A. Ivanov was partially supported by the Alexander von Humboldt Stiftung (Germany). S. Trofimchuk gratefully acknowledges the support of FONDECYT (Chile), project 1150480 as well as the NSERC research grant RGPIN-2015-05976 for partial support of travel expenses. Publisher Copyright: {\textcopyright} 2019 American Institute of Mathematical Sciences. All rights reserved.",
year = "2019",
doi = "10.3934/dcdss.2020017",
language = "English (US)",
volume = "13",
pages = "293--319",
journal = "Discrete and Continuous Dynamical Systems - Series S",
issn = "1937-1632",
publisher = "American Institute of Mathematical Sciences",
number = "2",
}