ON THE STUDY SYNCHRONIZATION OF A FORCED IMPULSIVE GOODWIN–SMITH OSCILLATOR
ON THE STUDY SYNCHRONIZATION OF A FORCED IMPULSIVE GOODWIN–SMITH OSCILLATOR
DOI:
https://doi.org/10.52754/16948645_2026_1(8)_60Keywords:
Goodwin–Smith oscillator, impulsive differential equation, forced synchronization, Arnold tongues.Abstract
In this paper we introduced a two-dimensional map to study the synchronization of a forced impulsive Goodwin–Smith oscillator. As a self-oscillatory system subjected to external periodic excitation, a scalar impulsive differential equation is considered. This equation adequately describes the phenomenon of oscillation locking in a modified Goodwin–Smith oscillator and allow us a detailed bifurcation analysis.
References
Lakshmikantham V., Bainov D. D., Simeonov P. S. Theory of Impulsive Differential Equations. Singapore: World Scientic; 1989. 273 p.
Churilov A., Medvedev A., Shepeljavyi A. Mathematical model of non-basal testosterone regulation in the male by pulse modulated feedback// Automatica. 2009. Vol. 45. No. 1. P. 78– 85. https://doi.org/10.1016/j.automatica.2008.06.016
Goodwin B. Oscillatory behaviour in enzymatic control processes// Adv. in Enzyme Regulation, 1965). Vol. 3. P. 425–438. https://doi.org/10.1016/0065-2571(65)90067-1
Smith W. R. Hypothalamic regulation of pituitary secretion of luteinizing hormoneii feedback control of gonadotropin secretion Bulletin of Mathematical Biology. 1980. Vol. 42(1). P. 57–78. https://doi.org/10.1007/BF02462366
Zhusubaliyev Zh. T., Churilov A., Medvedev A. Bifurcation phenomena in an impulsive model of non-basal testosterone regulation// Chaos. 2012. Vol. 22. No. 1. P. 013121. https://doi.org/10.1063/1.3685519
Zhusubaliyev Zh. T., Churilov A., Medvedev A. Complex dynamics and chaos in a scalar linear continuous system with impulsive feedback. Proc. of the 2012 American Control Conference, Montreal, Canada, 27–29 June, 2012. P. 2419–2424. DOI: 10.1109/ACC.2012.6314909
Zhusubaliyev Zh. T., Mosekilde E., Churilov A. N., Medvedev R. Multistability and hidden attractors in an impulsive Goodwin oscillator with time delay// Eur. Phys. J. Special Topics 2015. Vol. 224, P. 1519–1539. DOI: 10.1140/epjst/e2015–02477–8
Medvedev A., Proskurnikov A. V., Zhusubaliyev Zh.T. Mathematical modeling of endocrine regulation subject to circadian rhythm// Annual Reviews in Control . 2018. Vol.46. P. 148–164. https://doi.org//10.1016/j.arcontrol.2018.08.002
Pikovsky A., Rosenblum M., Kurths J. Synchronization: Universal Conception Nonlinear Science. Cambridge University Press, New York. 2001. 411 p.
Жусубалиев Ж. Т., Коломиец Е. A., Сопуев У. A., Цуканов Д. Ю., Иванова Е. Н., Цаньсин М., Цзылун Н. Отображение кольца для изучения вынужденной синхронизации импульсного осциллятора Гудвина// Международная научная конференция по механике «10 Поляховские чтения», 23–27 сентября 2024, СПбГУ, Санкт-Петербург. С. 602-606.
Афраймович В. С., Шильников Л. П. Инвариантные двумерные торы, их разрушение и стохастичность// Методы качественной теории дифференциальных уравнений: Межвуз. тематич. сб. науч. тр. / Е.А. Леонтович- Андронова. Горький: ГГУ. 1983. С. 3–6.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Journal of Osh State University. Mathematics. Physics. Technical Sciences
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
