First Integral Method for Evaluation of the Relations Between Components of Bray-Liebhafsky Models

The first integral method is used for transformation of the set of non-linear differential equations for the time evolution of components in Bray-Liebhafsky models. The capabilities for the method are demonstrated on the models proposed by Schmitz and Furrow. The method gives us time invariant relations between the components during the course of the process. They correspond to the conservation laws. The relations developed are allways linear; more precisely, we obtain alllinearly independent relations. As the result of the proposed transformations, the starting system is simplified to one with fewer number of non-linear differential equations and with complementary number of linear relations. In order to perform simplification, linear relations could be explicitly solved and substituted to the system. The method can be applied to any complex reaction model without any additional difficulty

The Bray-Liebhafsky oscillatory reaction: Kinetic investigations in reduction and oxidation pathways based on hydrogen peroxide concentration monitoring

By direct monitoring of the hydrogen concentration during its catalytic decomposition into water and oxygen in the presence of potassium iodate and sulfuric acid, that is in the Bray-Liebhafsky system, the pseudo-rate constants of overall reduction and oxidation pathways were determined The dependence of the obtained rate constants on acidity was evaluated. It was found that the pseudo-rate constant of the overall reduction process increases with increasing acidity, whereas the pseudo-rate constant of the overall oxidation process decreases with increasing acidity. The corresponding activation energies were also calculated using values of this constant at two temperatures.Direktnim praćenjem koncentracije vodonik-peroksida u toku njegovog katalitičkog razlaganja na vodu i kiseonik u prisustvu kalijum-jodata i sumporne kiseline, odnosno u Bray-Lievhafsky sistemu, analizirane su konstante brzina celokupnog redukcionog i oksidacionog puta kao konstante brzina pseudo-prvog reda. izvedene su njihove zavisnosti od kiselosti. Nađeno je da pseudo-konstanta brzine celokupnog redukcionog procesa raste sa porastom kiselosti, dok pseudo-konstanta brzine celokupnog oksidacionog procesa opada sa porastom kiselosti. korišćenjem njihovih vrednosti na dve temperature izračunate su odgovarajuće energije aktivacija

Influence of the form of the periodic function that describes the circadian rhythm of the hpa system activity

The influence of the form of the periodic function that describes the circadian rhythm on the hypothalamic-pituitary-adrenal (HPA) system self-regulatory activity in humans is discussed. It was found that the HPA system is very sensitive to the choice of this function since it moderates the concentration of all species that are included in the model, as well as the form of ultradian pulses.Physical chemistry 2006 : 8th international conference on fundamental and applied aspects of physical chemistry; Belgrade (Serbia); 26-29 September 200

Doprinosi Beogradske grupe izučavanju oscilatornih reakcija

Oscillatory dynamic states as one form of selforganization of nonlinear systems can be found in almost all sciences, like mechanics, physical chemistry or biomedicine. Although origin of these oscillations is different, computational challenges in modelling oscillatory phenomena remain similar in all fields. Since 1979 researchers from Belgrade's group perform systematic examinations of oscillatory reactions. As stability of steady states is the central point in modelling oscillatory reactions, in last 10 years they have adapted and improved powerful tool of the Stoichiometric Network Analysis for this goal. Moreover, bifurcations of few types were identified in several models of oscillatory reactions. Even very complex chaotic motions in phase space were characterized and quantified by several numerical techniques. Multiple time scale behaviour is found within the core of the complex dynamic behaviour of mixed-mode oscillations. Analytical applications were developed, too.Oscilatorna dinamička stanja, kao oblik samoorganizacije nelinearnih sistema, mogu se naći u gotovo svim naukama, kao što su mehanika, fizička hemija ili biomedicina. Iako je poreklo ovih oscilacija različito, teškoće u modeliranju oscilatornih fenomena su zajedničke na svim poljima. Od 1979. godine istraživači Beogradske grupe sistematski istražuju oscilatorne reakcije. Kako je stabilnost ustaljenih stanja ključni problem u modeliranju oscilatornih reakcija, u poslednjih 10 godina oni su za tu namenu usvojili i unapredili moćnu tehniku Analize stehiometrijskih mreža. Zatim je identifikovano više tipova bifurkacija u nekoliko modela oscilatornih reakcija. Čak su i veoma složena haotična kretanja u koncentracionom faznom prostoru okarakterisana i kvantifikovana različitim numeričkim tehnikama. Ustanovljeno je da izvor oscilacija mešanih modova i drugih uočenih složenih oblika dinamike predstavljaju procesi koji se odigravaju na različitim vremenskim skalama. Takođe su razvijene i analitičke primene oscilatornih reakcija

Belousov-Žabotinski oscilatorna reakcija - kinetika razlaganja malonske kiseline

The kinetics of the Belousov-Zhabotinsky (BZ) oscillatory reaction was analyzed. With this aim, the time evolution of a reaction mixture composed of malonic acid, bromate, sulfuric acid and cerium(III) was studied at 298 K. Pseudo-first order kinetics with respect to malonic acid as the species undergoing decomposition with a corresponding rate constant, k = 7.5x10-3 min-1, was found.Sa ciljem da se analizira kinetika Belousov-Žabotinski oscilatorne reakcije, proučavana je vremenska evolucija reakcione smeše koja se sastoji od malonske kiseline, sumporne kiseline i cerijuma(III) na 298 K. Nađena je kinetika pseudo-prvog reda u odnosu na malonsku kiselinu kao vrstu koja podleže razlaganju i odgovarajuća konstanta brzine, k = 7.5x10-3 min-1

The Bray-Liebhafsky oscillatory reaction: Kinetic investigations in reduction and oxidation pathways based on hydrogen peroxide concentration monitoring

By direct monitoring of the hydrogen concentration during its catalytic decomposition into water and oxygen in the presence of potassium iodate and sulfuric acid, that is in the Bray-Liebhafsky system, the pseudo-rate constants of overall reduction and oxidation pathways were determined The dependence of the obtained rate constants on acidity was evaluated. It was found that the pseudo-rate constant of the overall reduction process increases with increasing acidity, whereas the pseudo-rate constant of the overall oxidation process decreases with increasing acidity. The corresponding activation energies were also calculated using values of this constant at two temperatures.Direktnim praćenjem koncentracije vodonik-peroksida u toku njegovog katalitičkog razlaganja na vodu i kiseonik u prisustvu kalijum-jodata i sumporne kiseline, odnosno u Bray-Lievhafsky sistemu, analizirane su konstante brzina celokupnog redukcionog i oksidacionog puta kao konstante brzina pseudo-prvog reda. izvedene su njihove zavisnosti od kiselosti. Nađeno je da pseudo-konstanta brzine celokupnog redukcionog procesa raste sa porastom kiselosti, dok pseudo-konstanta brzine celokupnog oksidacionog procesa opada sa porastom kiselosti. korišćenjem njihovih vrednosti na dve temperature izračunate su odgovarajuće energije aktivacija

Stoichiometric network analysis as mathematical method for examinations of instability region and oscillatory dynamics

Reaction systems in chemistry, physical chemistry, and biochemistry, which can be described by true or pseudo-stoichiometric relationships between species, and, therefore, represented with stoichiometric models, are usually very complex. For the analysis of the models of these complex nonlinear reaction systems with more than three variables, which can be in different dynamic states like multistability, oscillatority or chaos, some general mathematical methods such as the Stoichiometric network analysis (SNA) must be used. Although the SNA is a powerful method for systematic examination of complex reaction systems, identification of underlying reaction pathways, and stability analysis of dynamic states, this method is practically unknown among mathematicians. Therefore, a simple application of SNA to one five-dimensional model is given here

Instability region in models of nonlinear reaction systems. The Stoichiometric Network Analysis

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.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

Stoichiometric network analysis of a reaction system with conservation constraints

Stoichiometric Network Analysis (SNA) is a powerful method that can be used to examine instabilities in modelling a broad range of reaction systems without knowing the explicit values of reaction rate constants. Due to a lack of understanding, SNA is rarely used and its full potential is not yet fulfilled. Using the oscillatory carbonylation of a polymeric substrate [poly(ethylene glycol) methyl ether acetylene] as a case study, in this work, we consider two mathematical methods for the application of SNA to the reaction models when conservation constraints between species have an important role. The first method takes conservation constraints into account and uses only independent intermediate species, while the second method applies to the full set of intermediate species, without the separation of independent and dependent variables. Both methods are used for examination of steady state stability by means of a characteristic polynomial and related Jacobian matrix. It was shown that both methods give the same results. Therefore, as the second method is simpler, we suggest it as a more straightforward method for the applications. Published by AIP Publishing