Instability region in models of nonlinear reaction systems. The Stoichiometric Network Analysis
2020
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Конференцијски прилог (Објављена верзија)
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Stability analysis of reaction systems is described by the application of the Stoichiometric Network Analysis to the three-variable-autocatalator. Although simple, this model is complex enough to describe complex forms of nonlinear dynamics phenomena, like mixed-mode oscillations and chaos. Therefore, stability analysis of such model is not a trivial task. Using the Stoichiometric Network Analysis for this purpose makes the process clear and leads to the reliable result.
The method is described briefly in few general steps and all of them are further clarified through the application to the chosen example. First, the reaction rates in steady state are decomposed to contributions of independent pathways, called extreme currents. Then, linearized operator is constructed. Finally, through the analysis of the principal minors of the essential part of this operator, simple stability criterion is identified.
Кључне речи:
Stoichiometric Network Analysis / three-variable-autocatalator / reaction systems / Stability analysisИзвор:
Proceedings - 1st Conference on nonlinearity, 2020, 145-159Издавач:
- Serbian academy of nonlinear sciences
Финансирање / пројекти:
- Динамика нелинеарних физичкохемијских и биохемијских система са моделирањем и предвиђањем њихових понашања под неравнотежним условима (RS-MESTD-Basic Research (BR or ON)-172015)
- Наноструктурни функционални и композитни материјали у каталитичким и сорпционим процесима (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-45001)
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200026 (Универзитет у Београду, Институт за хемију, технологију и металургију - ИХТМ) (RS-MESTD-inst-2020-200026)
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200146 (Универзитет у Београду, Факултет за физичку хемију) (RS-MESTD-inst-2020-200146)
Напомена:
- Organized on the occasion of the 110th anniversary since the birth of Nikolay Nikolaevich Bogolyubov, October 11–12, 2019, Belgrade, Serbia, published in 2020, Editors: B. Dragovich, Ž. Čupić,
Институција/група
IHTMTY - CONF AU - Čupić, Željko AU - Maćešić, Stevan AU - Kolar-Anić, Ljiljana PY - 2020 UR - https://cer.ihtm.bg.ac.rs/handle/123456789/3746 UR - http://imqf.ekof.bg.ac.rs/ConfNonlin/index.html AB - Stability analysis of reaction systems is described by the application of the Stoichiometric Network Analysis to the three-variable-autocatalator. Although simple, this model is complex enough to describe complex forms of nonlinear dynamics phenomena, like mixed-mode oscillations and chaos. Therefore, stability analysis of such model is not a trivial task. Using the Stoichiometric Network Analysis for this purpose makes the process clear and leads to the reliable result. The method is described briefly in few general steps and all of them are further clarified through the application to the chosen example. First, the reaction rates in steady state are decomposed to contributions of independent pathways, called extreme currents. Then, linearized operator is constructed. Finally, through the analysis of the principal minors of the essential part of this operator, simple stability criterion is identified. PB - Serbian academy of nonlinear sciences C3 - Proceedings - 1st Conference on nonlinearity T1 - Instability region in models of nonlinear reaction systems. The Stoichiometric Network Analysis SP - 145 EP - 159 UR - https://hdl.handle.net/21.15107/rcub_cer_3746 ER -
@conference{ author = "Čupić, Željko and Maćešić, Stevan and Kolar-Anić, Ljiljana", year = "2020", abstract = "Stability analysis of reaction systems is described by the application of the Stoichiometric Network Analysis to the three-variable-autocatalator. Although simple, this model is complex enough to describe complex forms of nonlinear dynamics phenomena, like mixed-mode oscillations and chaos. Therefore, stability analysis of such model is not a trivial task. Using the Stoichiometric Network Analysis for this purpose makes the process clear and leads to the reliable result. The method is described briefly in few general steps and all of them are further clarified through the application to the chosen example. First, the reaction rates in steady state are decomposed to contributions of independent pathways, called extreme currents. Then, linearized operator is constructed. Finally, through the analysis of the principal minors of the essential part of this operator, simple stability criterion is identified.", publisher = "Serbian academy of nonlinear sciences", journal = "Proceedings - 1st Conference on nonlinearity", title = "Instability region in models of nonlinear reaction systems. The Stoichiometric Network Analysis", pages = "145-159", url = "https://hdl.handle.net/21.15107/rcub_cer_3746" }
Čupić, Ž., Maćešić, S.,& Kolar-Anić, L.. (2020). Instability region in models of nonlinear reaction systems. The Stoichiometric Network Analysis. in Proceedings - 1st Conference on nonlinearity Serbian academy of nonlinear sciences., 145-159. https://hdl.handle.net/21.15107/rcub_cer_3746
Čupić Ž, Maćešić S, Kolar-Anić L. Instability region in models of nonlinear reaction systems. The Stoichiometric Network Analysis. in Proceedings - 1st Conference on nonlinearity. 2020;:145-159. https://hdl.handle.net/21.15107/rcub_cer_3746 .
Čupić, Željko, Maćešić, Stevan, Kolar-Anić, Ljiljana, "Instability region in models of nonlinear reaction systems. The Stoichiometric Network Analysis" in Proceedings - 1st Conference on nonlinearity (2020):145-159, https://hdl.handle.net/21.15107/rcub_cer_3746 .