Publication

Synchronization of Goodwin’s oscillators under boundedness and nonnegativeness constraints for solutions

Proskurnikov, A. V. & Cao, M., 2-Jan-2017, In : IEEE Transactions on Automatic Control. 62, 1, p. 372-378 7 p.

Research output: Contribution to journalArticleAcademicpeer-review

APA

Proskurnikov, A. V., & Cao, M. (2017). Synchronization of Goodwin’s oscillators under boundedness and nonnegativeness constraints for solutions. IEEE Transactions on Automatic Control, 62(1), 372-378. https://doi.org/10.1109/TAC.2016.2524998

Author

Proskurnikov, Anton V. ; Cao, Ming. / Synchronization of Goodwin’s oscillators under boundedness and nonnegativeness constraints for solutions. In: IEEE Transactions on Automatic Control. 2017 ; Vol. 62, No. 1. pp. 372-378.

Harvard

Proskurnikov, AV & Cao, M 2017, 'Synchronization of Goodwin’s oscillators under boundedness and nonnegativeness constraints for solutions', IEEE Transactions on Automatic Control, vol. 62, no. 1, pp. 372-378. https://doi.org/10.1109/TAC.2016.2524998

Standard

Synchronization of Goodwin’s oscillators under boundedness and nonnegativeness constraints for solutions. / Proskurnikov, Anton V.; Cao, Ming.

In: IEEE Transactions on Automatic Control, Vol. 62, No. 1, 02.01.2017, p. 372-378.

Research output: Contribution to journalArticleAcademicpeer-review

Vancouver

Proskurnikov AV, Cao M. Synchronization of Goodwin’s oscillators under boundedness and nonnegativeness constraints for solutions. IEEE Transactions on Automatic Control. 2017 Jan 2;62(1):372-378. https://doi.org/10.1109/TAC.2016.2524998


BibTeX

@article{a4e7935af38b4202aeb3df43dd290e05,
title = "Synchronization of Goodwin’s oscillators under boundedness and nonnegativeness constraints for solutions",
abstract = "In the recent paper by Hamadeh et al. (2012) an elegant analytic criterion for incremental output feedback passivity (iOFP) of cyclic feedback systems (CFS) has been reported, assuming that the constituent subsystems are incrementally output strictly passive (iOSP). This criterion was used to prove that a network of identical CFS can be synchronized under sufficiently strong linear diffusive coupling. A very important class of CFS consists of biological oscillators, named after Brian Goodwin and describing self-regulated chains of enzymatic reactions, where the product of each reaction catalyzes the next reaction in the chain, however, the last product inhibits the first reaction in the chain. Goodwin’s oscillators are used to model the dynamics of genetic circadian pacemakers, hormonal cycles and some metabolic pathways. In this paper we show that for Goodwin’s oscillators, where the individual reactions have nonlinear (e.g. Mikhaelis-Menten) kinetics, the synchronization criterion, obtained by Hamadeh et al., cannot be directly applied. This criterion relies on the implicit assumption of the solution boundedness, dictated also by the chemical feasibility (the state variables stand for the concentrations of chemicals). Furthermore, to test the synchronization condition one needs to know an explicit bound for a solution, which generally cannot be guaranteed under linear coupling. At the same time, we show that these restrictions can be avoided for a nonlinear coupling protocol, where the control inputs are saturated by a special nonlinear function (belonging to a wide class), which guarantees nonnegativity of the solutions and allows to get explicit ultimate bounds for them. We prove that oscillators synchronize under such a protocol, provided that the couplings are sufficiently strong.",
author = "Proskurnikov, {Anton V.} and Ming Cao",
year = "2017",
month = "1",
day = "2",
doi = "10.1109/TAC.2016.2524998",
language = "English",
volume = "62",
pages = "372--378",
journal = "IEEE-Transactions on Automatic Control",
issn = "0018-9286",
publisher = "IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC",
number = "1",

}

RIS

TY - JOUR

T1 - Synchronization of Goodwin’s oscillators under boundedness and nonnegativeness constraints for solutions

AU - Proskurnikov, Anton V.

AU - Cao, Ming

PY - 2017/1/2

Y1 - 2017/1/2

N2 - In the recent paper by Hamadeh et al. (2012) an elegant analytic criterion for incremental output feedback passivity (iOFP) of cyclic feedback systems (CFS) has been reported, assuming that the constituent subsystems are incrementally output strictly passive (iOSP). This criterion was used to prove that a network of identical CFS can be synchronized under sufficiently strong linear diffusive coupling. A very important class of CFS consists of biological oscillators, named after Brian Goodwin and describing self-regulated chains of enzymatic reactions, where the product of each reaction catalyzes the next reaction in the chain, however, the last product inhibits the first reaction in the chain. Goodwin’s oscillators are used to model the dynamics of genetic circadian pacemakers, hormonal cycles and some metabolic pathways. In this paper we show that for Goodwin’s oscillators, where the individual reactions have nonlinear (e.g. Mikhaelis-Menten) kinetics, the synchronization criterion, obtained by Hamadeh et al., cannot be directly applied. This criterion relies on the implicit assumption of the solution boundedness, dictated also by the chemical feasibility (the state variables stand for the concentrations of chemicals). Furthermore, to test the synchronization condition one needs to know an explicit bound for a solution, which generally cannot be guaranteed under linear coupling. At the same time, we show that these restrictions can be avoided for a nonlinear coupling protocol, where the control inputs are saturated by a special nonlinear function (belonging to a wide class), which guarantees nonnegativity of the solutions and allows to get explicit ultimate bounds for them. We prove that oscillators synchronize under such a protocol, provided that the couplings are sufficiently strong.

AB - In the recent paper by Hamadeh et al. (2012) an elegant analytic criterion for incremental output feedback passivity (iOFP) of cyclic feedback systems (CFS) has been reported, assuming that the constituent subsystems are incrementally output strictly passive (iOSP). This criterion was used to prove that a network of identical CFS can be synchronized under sufficiently strong linear diffusive coupling. A very important class of CFS consists of biological oscillators, named after Brian Goodwin and describing self-regulated chains of enzymatic reactions, where the product of each reaction catalyzes the next reaction in the chain, however, the last product inhibits the first reaction in the chain. Goodwin’s oscillators are used to model the dynamics of genetic circadian pacemakers, hormonal cycles and some metabolic pathways. In this paper we show that for Goodwin’s oscillators, where the individual reactions have nonlinear (e.g. Mikhaelis-Menten) kinetics, the synchronization criterion, obtained by Hamadeh et al., cannot be directly applied. This criterion relies on the implicit assumption of the solution boundedness, dictated also by the chemical feasibility (the state variables stand for the concentrations of chemicals). Furthermore, to test the synchronization condition one needs to know an explicit bound for a solution, which generally cannot be guaranteed under linear coupling. At the same time, we show that these restrictions can be avoided for a nonlinear coupling protocol, where the control inputs are saturated by a special nonlinear function (belonging to a wide class), which guarantees nonnegativity of the solutions and allows to get explicit ultimate bounds for them. We prove that oscillators synchronize under such a protocol, provided that the couplings are sufficiently strong.

U2 - 10.1109/TAC.2016.2524998

DO - 10.1109/TAC.2016.2524998

M3 - Article

VL - 62

SP - 372

EP - 378

JO - IEEE-Transactions on Automatic Control

JF - IEEE-Transactions on Automatic Control

SN - 0018-9286

IS - 1

ER -

ID: 27641942