TY  - JOUR
AU  - Čupić, Željko
AU  - Ivanović-Šašić, Ana
AU  - Anić, Slobodan
AU  - Stankovic, Branislav
AU  - Maksimović, Jelena
AU  - Kolar-Anić, Ljiljana
AU  - Schmitz, Guy
PY  - 2013
UR  - https://cer.ihtm.bg.ac.rs/handle/123456789/1183
AB  - The mixed-mode dynamical states found experimentally in the concentration phase space of the iodate catalyzed hydrogen peroxide decomposition (The Bray-Liebhafsky oscillatory reaction) are discussed theoretically in a related multiple-time-scale model, from the viewpoint of tourbillion. With aim to explain the mixed-mode oscillations obtained by numerical simulations of the various dynamical states of a model for the Bray-Liebhafsky reaction under CSTR conditions, the folded singularity points on the critical manifold of the full system and Andronov-Hopf bifurcation of the fast subsystem are calculated. The interaction between those singularities causes occurrence of tourbillion structure.
PB  - Univ Kragujevac, Fac Science, Kragujevac
T2  - Match-Communications in Mathematical and in Computer Chemistry
T1  - Tourbillion in the phase space of the Bray-Liebhafsky nonlinear oscillatory reaction and related multiple-time-scale model
VL  - 69
IS  - 3
SP  - 805
EP  - 830
UR  - https://hdl.handle.net/21.15107/rcub_cer_1183
ER  - 

@article{
author = "Čupić, Željko and Ivanović-Šašić, Ana and Anić, Slobodan and Stankovic, Branislav and Maksimović, Jelena and Kolar-Anić, Ljiljana and Schmitz, Guy",
year = "2013",
abstract = "The mixed-mode dynamical states found experimentally in the concentration phase space of the iodate catalyzed hydrogen peroxide decomposition (The Bray-Liebhafsky oscillatory reaction) are discussed theoretically in a related multiple-time-scale model, from the viewpoint of tourbillion. With aim to explain the mixed-mode oscillations obtained by numerical simulations of the various dynamical states of a model for the Bray-Liebhafsky reaction under CSTR conditions, the folded singularity points on the critical manifold of the full system and Andronov-Hopf bifurcation of the fast subsystem are calculated. The interaction between those singularities causes occurrence of tourbillion structure.",
publisher = "Univ Kragujevac, Fac Science, Kragujevac",
journal = "Match-Communications in Mathematical and in Computer Chemistry",
title = "Tourbillion in the phase space of the Bray-Liebhafsky nonlinear oscillatory reaction and related multiple-time-scale model",
volume = "69",
number = "3",
pages = "805-830",
url = "https://hdl.handle.net/21.15107/rcub_cer_1183"
}

Čupić, Ž., Ivanović-Šašić, A., Anić, S., Stankovic, B., Maksimović, J., Kolar-Anić, L.,& Schmitz, G.. (2013). Tourbillion in the phase space of the Bray-Liebhafsky nonlinear oscillatory reaction and related multiple-time-scale model. in Match-Communications in Mathematical and in Computer Chemistry
Univ Kragujevac, Fac Science, Kragujevac., 69(3), 805-830.
https://hdl.handle.net/21.15107/rcub_cer_1183

Čupić Ž, Ivanović-Šašić A, Anić S, Stankovic B, Maksimović J, Kolar-Anić L, Schmitz G. Tourbillion in the phase space of the Bray-Liebhafsky nonlinear oscillatory reaction and related multiple-time-scale model. in Match-Communications in Mathematical and in Computer Chemistry. 2013;69(3):805-830.
https://hdl.handle.net/21.15107/rcub_cer_1183 .

Čupić, Željko, Ivanović-Šašić, Ana, Anić, Slobodan, Stankovic, Branislav, Maksimović, Jelena, Kolar-Anić, Ljiljana, Schmitz, Guy, "Tourbillion in the phase space of the Bray-Liebhafsky nonlinear oscillatory reaction and related multiple-time-scale model" in Match-Communications in Mathematical and in Computer Chemistry, 69, no. 3 (2013):805-830,
https://hdl.handle.net/21.15107/rcub_cer_1183 .

TY  - CONF
AU  - Ivanović, Ana
AU  - Čupić, Željko
AU  - Marinović, Sanja
AU  - Schmitz, Guy
AU  - Kolar-Anić, Ljiljana
PY  - 2010
UR  - https://cer.ihtm.bg.ac.rs/handle/123456789/6317
AB  - Mixed mode oscillations are obtained in numerical simulations of the Bray-
Liebhafsky oscillatory reaction in CSTR, for appropriate choice of the parameter
set. In this paper, we analyze critical manifold of the slow-fast system in three
dimensional phase subspace. We found that small amplitude oscillations obtained
as a part of mixed mode dynamics are governed by canard solutions.
PB  - Society of Physical Chemists of Serbia
C3  - Proceedings - 10th International Conference on Fundamental and Applied Aspects of Physical Chemistry, Physical Chemistry 2010, 21-24 September 2010, Belgrade, Serbia
T1  - Critical manifold of the model for Bray-Liebhafsky oscillatory reaction
SP  - 236
EP  - 238
UR  - https://hdl.handle.net/21.15107/rcub_cer_6317
ER  - 

@conference{
author = "Ivanović, Ana and Čupić, Željko and Marinović, Sanja and Schmitz, Guy and Kolar-Anić, Ljiljana",
year = "2010",
abstract = "Mixed mode oscillations are obtained in numerical simulations of the Bray-
Liebhafsky oscillatory reaction in CSTR, for appropriate choice of the parameter
set. In this paper, we analyze critical manifold of the slow-fast system in three
dimensional phase subspace. We found that small amplitude oscillations obtained
as a part of mixed mode dynamics are governed by canard solutions.",
publisher = "Society of Physical Chemists of Serbia",
journal = "Proceedings - 10th International Conference on Fundamental and Applied Aspects of Physical Chemistry, Physical Chemistry 2010, 21-24 September 2010, Belgrade, Serbia",
title = "Critical manifold of the model for Bray-Liebhafsky oscillatory reaction",
pages = "236-238",
url = "https://hdl.handle.net/21.15107/rcub_cer_6317"
}

Ivanović, A., Čupić, Ž., Marinović, S., Schmitz, G.,& Kolar-Anić, L.. (2010). Critical manifold of the model for Bray-Liebhafsky oscillatory reaction. in Proceedings - 10th International Conference on Fundamental and Applied Aspects of Physical Chemistry, Physical Chemistry 2010, 21-24 September 2010, Belgrade, Serbia
Society of Physical Chemists of Serbia., 236-238.
https://hdl.handle.net/21.15107/rcub_cer_6317

Ivanović A, Čupić Ž, Marinović S, Schmitz G, Kolar-Anić L. Critical manifold of the model for Bray-Liebhafsky oscillatory reaction. in Proceedings - 10th International Conference on Fundamental and Applied Aspects of Physical Chemistry, Physical Chemistry 2010, 21-24 September 2010, Belgrade, Serbia. 2010;:236-238.
https://hdl.handle.net/21.15107/rcub_cer_6317 .

Ivanović, Ana, Čupić, Željko, Marinović, Sanja, Schmitz, Guy, Kolar-Anić, Ljiljana, "Critical manifold of the model for Bray-Liebhafsky oscillatory reaction" in Proceedings - 10th International Conference on Fundamental and Applied Aspects of Physical Chemistry, Physical Chemistry 2010, 21-24 September 2010, Belgrade, Serbia (2010):236-238,
https://hdl.handle.net/21.15107/rcub_cer_6317 .

TY  - JOUR
AU  - Kolar-Anić, Ljiljana
AU  - Čupić, Željko
AU  - Schmitz, Guy
AU  - Anić, Slobodan
PY  - 2010
UR  - https://cer.ihtm.bg.ac.rs/handle/123456789/633
AB  - Stoichiometric network analysis (SNA), a known method for analyzing complex reaction systems including biochemical ones, is improved and applied to a nonlinear process studied far from equilibrium in a continuously fed, well stirred tank reactor (CSTR). A particular attention is focused on the determination of the narrow range of the control parameter values where the main steady state is unstable and where different dynamic states can be simulated numerically. The instability region, the most important feature of nonlinear reaction systems, is calculated as a function of the SNA parameters (current rates and reciprocal concentrations of intermediate species in the steady state) and simplified by retaining only the dominant terms. Since the number of the current rates is usually larger than the number of linearly independent equations to be used for their calculation, it is shown here that the current rates can be replaced with a smaller number of reaction rates at the steady state. These rates are related to the experimental data in a simple manner. The instability conditions is also written as a function of dimensionless parameters derived from the SNA. This general approach is applied to a model of the Bray-Liebhafsky (BL) reaction having seven reactions without direct autocatalysis or autoinhibition, studied under CSTR conditions. Since the model has six intermediate species, it would be very difficult to analyze its instability condition by the conventional procedure, where a sixth order characteristics equation would have to be solved. On the other hand, the instability condition, obtained easily by the improved SNA, locates correctly the oscillatory region using numerical integration. Other dynamic states found earlier with a larger model of the BL reaction, such as mixed-mode oscillations, period doubling and chaos, are also obtained within the theoretically predicted oscillatory region. Thus, besides the general advantages of the improved stoichiometric network analysis as a method appropriate for the examination of complex nonlinear reactions, we show that the various mentioned dynamic states can be obtained by a very simple variant of the model of the BL reaction realized under CSTR conditions.
PB  - Oxford : Pergamon-Elsevier Science Ltd
T2  - Chemical Engineering Science
T1  - Improvement of the stoichiometric network analysis for determination of instability conditions of complex nonlinear reaction systems
VL  - 65
IS  - 12
SP  - 3718
EP  - 3728
DO  - 10.1016/j.ces.2010.03.008
ER  - 

@article{
author = "Kolar-Anić, Ljiljana and Čupić, Željko and Schmitz, Guy and Anić, Slobodan",
year = "2010",
abstract = "Stoichiometric network analysis (SNA), a known method for analyzing complex reaction systems including biochemical ones, is improved and applied to a nonlinear process studied far from equilibrium in a continuously fed, well stirred tank reactor (CSTR). A particular attention is focused on the determination of the narrow range of the control parameter values where the main steady state is unstable and where different dynamic states can be simulated numerically. The instability region, the most important feature of nonlinear reaction systems, is calculated as a function of the SNA parameters (current rates and reciprocal concentrations of intermediate species in the steady state) and simplified by retaining only the dominant terms. Since the number of the current rates is usually larger than the number of linearly independent equations to be used for their calculation, it is shown here that the current rates can be replaced with a smaller number of reaction rates at the steady state. These rates are related to the experimental data in a simple manner. The instability conditions is also written as a function of dimensionless parameters derived from the SNA. This general approach is applied to a model of the Bray-Liebhafsky (BL) reaction having seven reactions without direct autocatalysis or autoinhibition, studied under CSTR conditions. Since the model has six intermediate species, it would be very difficult to analyze its instability condition by the conventional procedure, where a sixth order characteristics equation would have to be solved. On the other hand, the instability condition, obtained easily by the improved SNA, locates correctly the oscillatory region using numerical integration. Other dynamic states found earlier with a larger model of the BL reaction, such as mixed-mode oscillations, period doubling and chaos, are also obtained within the theoretically predicted oscillatory region. Thus, besides the general advantages of the improved stoichiometric network analysis as a method appropriate for the examination of complex nonlinear reactions, we show that the various mentioned dynamic states can be obtained by a very simple variant of the model of the BL reaction realized under CSTR conditions.",
publisher = "Oxford : Pergamon-Elsevier Science Ltd",
journal = "Chemical Engineering Science",
title = "Improvement of the stoichiometric network analysis for determination of instability conditions of complex nonlinear reaction systems",
volume = "65",
number = "12",
pages = "3718-3728",
doi = "10.1016/j.ces.2010.03.008"
}

Kolar-Anić, L., Čupić, Ž., Schmitz, G.,& Anić, S.. (2010). Improvement of the stoichiometric network analysis for determination of instability conditions of complex nonlinear reaction systems. in Chemical Engineering Science
Oxford : Pergamon-Elsevier Science Ltd., 65(12), 3718-3728.
https://doi.org/10.1016/j.ces.2010.03.008

Kolar-Anić L, Čupić Ž, Schmitz G, Anić S. Improvement of the stoichiometric network analysis for determination of instability conditions of complex nonlinear reaction systems. in Chemical Engineering Science. 2010;65(12):3718-3728.
doi:10.1016/j.ces.2010.03.008 .

Kolar-Anić, Ljiljana, Čupić, Željko, Schmitz, Guy, Anić, Slobodan, "Improvement of the stoichiometric network analysis for determination of instability conditions of complex nonlinear reaction systems" in Chemical Engineering Science, 65, no. 12 (2010):3718-3728,
https://doi.org/10.1016/j.ces.2010.03.008 . .

TY  - JOUR
AU  - Schmitz, Guy
AU  - Kolar-Anić, Ljiljana
AU  - Anić, Slobodan
AU  - Čupić, Željko
PY  - 2008
UR  - https://cer.ihtm.bg.ac.rs/handle/123456789/385
AB  - The stoichiometric network analysis (SNA) introduced by B. L. Clarke is applied to a simplified model of the complex oscillating Bray-Liebhafsky reaction under batch conditions, which was not examined by this method earlier. This powerful method for the analysis of steady-states stability is also used to transform the classical differential equations into dimensionless equations. This transformation is easy and leads to a form of the equations combining the advantages of classical dimensionless equations with the advantages of the SNA. The used dimensionless parameters have orders of magnitude given by the experimental information about concentrations and currents. This simplifies greatly the study of the slow manifold and shows which parameters are essential for controlling its shape and consequently have an important influence oil the trajectories. The effectiveness of these equations is illustrated on two examples: the study of the bifurcations points and a simple sensitivity analysis, different from the classical one, more based on the chemistry of the studied system.
PB  - American Chemical Society (ACS)
T2  - Journal of Physical Chemistry A
T1  - Stoichiometric Network Analysis and Associated Dimensionless Kinetic Equations. Application to a Model of the Bray-Liebhafsky Reaction
VL  - 112
IS  - 51
SP  - 13452
EP  - 13457
DO  - 10.1021/jp8056674
ER  - 

@article{
author = "Schmitz, Guy and Kolar-Anić, Ljiljana and Anić, Slobodan and Čupić, Željko",
year = "2008",
abstract = "The stoichiometric network analysis (SNA) introduced by B. L. Clarke is applied to a simplified model of the complex oscillating Bray-Liebhafsky reaction under batch conditions, which was not examined by this method earlier. This powerful method for the analysis of steady-states stability is also used to transform the classical differential equations into dimensionless equations. This transformation is easy and leads to a form of the equations combining the advantages of classical dimensionless equations with the advantages of the SNA. The used dimensionless parameters have orders of magnitude given by the experimental information about concentrations and currents. This simplifies greatly the study of the slow manifold and shows which parameters are essential for controlling its shape and consequently have an important influence oil the trajectories. The effectiveness of these equations is illustrated on two examples: the study of the bifurcations points and a simple sensitivity analysis, different from the classical one, more based on the chemistry of the studied system.",
publisher = "American Chemical Society (ACS)",
journal = "Journal of Physical Chemistry A",
title = "Stoichiometric Network Analysis and Associated Dimensionless Kinetic Equations. Application to a Model of the Bray-Liebhafsky Reaction",
volume = "112",
number = "51",
pages = "13452-13457",
doi = "10.1021/jp8056674"
}

Schmitz, G., Kolar-Anić, L., Anić, S.,& Čupić, Ž.. (2008). Stoichiometric Network Analysis and Associated Dimensionless Kinetic Equations. Application to a Model of the Bray-Liebhafsky Reaction. in Journal of Physical Chemistry A
American Chemical Society (ACS)., 112(51), 13452-13457.
https://doi.org/10.1021/jp8056674

Schmitz G, Kolar-Anić L, Anić S, Čupić Ž. Stoichiometric Network Analysis and Associated Dimensionless Kinetic Equations. Application to a Model of the Bray-Liebhafsky Reaction. in Journal of Physical Chemistry A. 2008;112(51):13452-13457.
doi:10.1021/jp8056674 .

Schmitz, Guy, Kolar-Anić, Ljiljana, Anić, Slobodan, Čupić, Željko, "Stoichiometric Network Analysis and Associated Dimensionless Kinetic Equations. Application to a Model of the Bray-Liebhafsky Reaction" in Journal of Physical Chemistry A, 112, no. 51 (2008):13452-13457,
https://doi.org/10.1021/jp8056674 . .