Oscillations in Low-Dimensional Cyclic Differential Delay Systems

Anatoli 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
Volume259
ISBN (Print)9783319997186
DOIs
StatePublished - Jan 1 2018
EventInternational conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2017 - Waterloo, Canada
Duration: Aug 20 2017Aug 25 2017

Other

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

Fingerprint

Delay-differential Systems
Oscillation
Mathematical Biology
Negative Feedback
Life sciences
Physiology
Optics
Open Problems
High-dimensional
Physics
Economics
Mathematical Model
Laser
Differential equation
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Ivanov, A., & 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 (Vol. 259, pp. 603-613). Springer New York LLC. https://doi.org/10.1007/978-3-319-99719-3_54
Ivanov, Anatoli ; Dzalilov, Zari A. / Oscillations in Low-Dimensional Cyclic Differential Delay Systems. Recent Advances in Mathematical and Statistical Methods - IV AMMCS International Conference. editor / Herb Kunze ; D. Marc Kilgour ; Roman Makarov ; Roderick Melnik ; Xu Wang. Vol. 259 Springer New York LLC, 2018. pp. 603-613
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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.",
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Ivanov, A & Dzalilov, ZA 2018, Oscillations in Low-Dimensional Cyclic Differential Delay Systems. in H Kunze, DM Kilgour, R Makarov, R Melnik & X Wang (eds), Recent Advances in Mathematical and Statistical Methods - IV AMMCS International Conference. vol. 259, Springer New York LLC, pp. 603-613, International conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2017, Waterloo, Canada, 8/20/17. https://doi.org/10.1007/978-3-319-99719-3_54

Oscillations in Low-Dimensional Cyclic Differential Delay Systems. / Ivanov, Anatoli; Dzalilov, Zari A.

Recent Advances in Mathematical and Statistical Methods - IV AMMCS International Conference. ed. / Herb Kunze; D. Marc Kilgour; Roman Makarov; Roderick Melnik; Xu Wang. Vol. 259 Springer New York LLC, 2018. p. 603-613.

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

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N2 - 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.

AB - 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.

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Ivanov A, Dzalilov ZA. Oscillations in Low-Dimensional Cyclic Differential Delay Systems. In Kunze H, Kilgour DM, Makarov R, Melnik R, Wang X, editors, Recent Advances in Mathematical and Statistical Methods - IV AMMCS International Conference. Vol. 259. Springer New York LLC. 2018. p. 603-613 https://doi.org/10.1007/978-3-319-99719-3_54