Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
In stoichiometric network analysis (SNA) the instability condition is calculated by the current rates. Recently, we have shown that in the final result the current rates can be substituted by reaction rates, which is a more appropriate value for the examination of instability from experimental point of view. Here, we elaborate the problem of whether the current rates are necessary parameters in the calculation, with the aim of obtaining the region of instability. All calculations are performed on a model for Belousov-Zhabotinsky (BZ) reaction, which has not been examined by SNA.
Czasopismo
Rocznik
Tom
Numer
Opis fizyczny
Daty
otrzymano
2013-10-30
zaakceptowano
2014-09-30
online
2014-12-23
Twórcy
autor
-
Faculty of Physical
Chemistry, University of Belgrade, Studentski trg 12-16,
11000 Belgrade, Serbia
autor
-
University of Belgrade,
Institute of Chemistry, Technology and Metallurgy, Department
of Catalysis and Chemical Engineering, Njegoševa 12, 11000
Belgrade, Serbia
autor
-
Faculty of Pharmacy,
Department of Physical Chemistry and Instrumental Analysis,
University of Belgrade, Vojvode Stepe 450, 11000 Belgrade, Serbia
autor
-
Faculty of Pharmacy,
Department of Physical Chemistry and Instrumental Analysis,
University of Belgrade, Vojvode Stepe 450, 11000 Belgrade, Serbia
autor
-
Faculty of Physical
Chemistry, University of Belgrade, Studentski trg 12-16,
11000 Belgrade, Serbia
autor
-
Faculty of Physical
Chemistry, University of Belgrade, Studentski trg 12-16,
11000 Belgrade, Serbia -
University of Belgrade,
Institute of Chemistry, Technology and Metallurgy, Department
of Catalysis and Chemical Engineering, Njegoševa 12, 11000
Belgrade, Serbia
Bibliografia
- [1] Gray P., Scott S.K., Chemical oscillations and instabilities,Clarendon Press, Oxford, 1990.
- [2] Scott S.K., Chemical chaos, Clarendon Press, Oxford, 1991.
- [3] Drazin P.G., Nonlinear systems, Cambridge University Press,1994.
- [4] Nicolis G., Introduction to nonlinear science, CambridgeUniversity Press, Cambridge, 1995.
- [5] Heinrich R., Schuster S., The regulation of cellular systems,Chapman & Hall, New York, 1996.
- [6] Epstein I.R., Pojman J.A., An Introduction to nonlinear chemicaldynamics : oscillations, waves, patterns, and chaos, OxfordUniversity Press, Oxford, 1998.
- [7] Ross J., Schreiber I., Vlad M.O., Determination of complexreaction mechanisms : Analysis of chemical, biological, andgenetic networks, Oxford University Press, Oxford, 2006.
- [8] Sun J.Q., Luo A.C.J., Bifurcation and chaos in complex systems,Elsevier, 2006.
- [9] Domijan M., Kirkilionis M., Bistability and oscillations inchemical reaction networks, J. Math. Biol., 2009, 59, 467-501.
- [10] Palsson B., Systems Biology: Simulation of dynamic networkstates, Cambridge University Press, Cambridge, 2011.
- [11] Čupić Ž., Ivanović-Šašić A., Anić S., Stanković B., Maksimović J.,Kolar-Anić L., Schmmitz G., Tourbillion in the phase space ofthe Bray-Liebhafsky nonlinear oscillatory reaction and relatedmultiple-time-scale model, MATCH, 2013, 69, 805-830.
- [12] Clarke B.L., in:, I. Prigogine, S.A. Rice (Eds.), Advances inchemical physics, John Wiley & Sons, Inc., 1980, 1–215.
- [13] Kolar-Anić L., Čupić Ž., Schmitz G., Anić S., Improvement of thestoichiometric network analysis for determination of instabilityconditions of complex nonlinear reaction systems, Chem. Eng.Sci., 2010, 65, 3718-3728[Crossref]
- [14] Blagojević S.M., Anić S., Čupić Ž., Pejić N., Kolar-Anić L., Malonicacid concentration as a control parameter in the kinetic analysisof the Belousov–Zhabotinsky reaction under batch conditions,Phys. Chem. Chem. Phys., 2008, 10, 6658-6664.[Crossref]
- [15] Belousov B.P., Sb. Ref. Radiat. Med. (collections of abstracts onradiation medicine), Medgiz, Moscow, 1958, 145–147.
- [16] Zhabotinsky A., Periodical oxidation of malonic acid in solution(a study of the Belousov reaction kinetics),Biofizika, 1964, 9,306-311.
- [17] Field R.J., Burger B., Oscillations and traveling waves in chemicalsystem, Mir, Moscow, 1988, 78–116.
- [18] Schmitz R.A., Graziani K.R., Hudson J.L., Experimental evidenceof chaotic states in the Belousov–Zhabotinskii reaction,J. Chem. Phys., 1977, 67, 3040-3044.
- [19] Wang J., Soerensen P.G., Hynne F., Transient period doublings,torus oscillations, and chaos in a closed chemical system,J. Phys. Chem., 1994,98, 725-727.[Crossref]
- [20] Strizhak P.E., Kawczynski A.L., Complex transient oscillations inthe belousov- zhabotinskii reaction in a batch reactor, J. Phys.Chem., 1995, 99, 10830-10833.[Crossref]
- [21] Rachwalska M., Kawczyński A.L., New types of mixed-modeperiodic oscillations in the Belousov−Zhabotinsky reaction incontinuously stirred tank reactors, J. Phys. Chem. A, 1999, 103,3455-3457.
- [22] Field R.J., Koros E., Noyes R.M., Oscillations in chemicalsystems. II. Thorough analysis of temporal oscillation in thebromate-cerium-malonic acid system, J. Am. Chem. Soc., 1972,94, 8649-8664.[Crossref]
- [23] Field R.J., Limit cycle oscillations in the reversible Oregonator,J. Chem. Phys., 1975, 63, 2289-2296.
- [24] Showalter K., Noyes R.M., Bar-Eli K., A modified Oregonatormodel exhibiting complicated limit cycle behavior in a flowsystem, J. Chem. Phys., 1978, 69, 2514-2524.
- [25] Bar-Eli K., Noyes R.M., Computations simulating experimentalobservations of complex bursting patterns in the Belousov–Zhabotinsky system, J. Chem. Phys., 1988, 88, 3646– 3655.
- [26] Försterling H.D., Murányi S., Noszticzius Z., The role of radicalsin the Belousov- Zhabotinsky reaction, React. Kinet. Catal. L.,1990, 42, 217-226.[Crossref]
- [27] Gyorgyi L., Turanyi T., Field R.J., Mechanistic details of theoscillatory Belousov- Zhabotinskii reaction, J. Phys. Chem.,1990, 94, 7162-7170.[Crossref]
- [28] Gyorgyi L., Rempe S.L., Field R.J., A novel model for thesimulation of chaos in low- flow-rate CSTR experiments with theBelousov-Zhabotinskii reaction: a chemical mechanism for twofrequencyoscillations, J. Phys. Chem., 1991, 95, 3159-3165.[Crossref]
- [29] Ševčíková H., Schreiber I., Marek M., Dynamics of oxidationBelousov-Zhabotinsky wawes in an electric field, J. Phys.Chem., 1996, 100, 19153-19164.[Crossref]
- [30] Johnson B.R., Scott S.K., Thompson B.W., Modelling complextransient oscillations for the BZ reaction in a batch reactor,Chaos, 1997, 7, 350-358.[Crossref]
- [31] Hegedús L., Wittmann M., Noszticzius Z., Yan S., SirimungkalaA., Försterling H.D., Field R.J., HPLC analysis of complete BZsystems. Evolution of the chemical composition in cerium andferroin catalysed batch oscillators: experiments and modelcalculations, Faraday Discuss., 2001, 120, 21-38.
- [32] Strizak P.E., Детерминований Хаос в Хімії, Академперіодика,Кїев, 2002.
- [33] Davies M.L., Schreiber I., Scott S.K., Dynamical behaviour of theBelousov– Zhabotinsky reaction in a fed-batch reactor, Chem.Eng. Sci., 2004, 59, 139-148.
- [34] Blagojević S.M., Anić S.R., Čupić Ž.D., Pejić N.D., Kolar-AnićL.Z., Temperature influence on the malonic acid decompositionin the Belousov-Zhabotinsky reaction, Russ. J. Phys. Chem. A,2009, 83, 1496-1501.
- [35] Gaspar V., Bazsa G., Beck M.T., Bistability and bromidecontrolledoscillation during bromate oxidation of ferroin ina continuous flow stirred tank reactor, J. Phys. Chem., 1985, 89,5495-5499.[Crossref]
- [36] Noszticzius Z., Stirling P., Wittmann M., Measurement ofbromine removal rate in the oscillatory BZ reaction of oxalicacid. Transition from limit cycle oscillations to excitability via saddle-node infinite period bifurcation, J. Phys. Chem., 1985,89, 4914- 4921.[Crossref]
- [37] Gaspar V., Galambosi P., Bifurcation diagram of the oscillatoryBelousov-Zhabotinskii system of oxalic acid in a continuousflow stirred tank reactor. Further possible evidence of saddlenode infinite period bifurcation behavior of the system, J. Phys.Chem., 1986, 90, 2222-2226.[Crossref]
- [38] Robertson E.B., Dunford H.B., The state of the proton in aqueoussulfuric acid, J. Am. Chem. Soc., 1964, 86, 5080-5089.[Crossref]
- [39] Clarke B.L., Stoichiometric network analysis, Cell Biophys.,1988, 12, 237-253.[Crossref]
- [40] Strogatz S.H., Nonlinear dynamics and chaos: with applicationsto physics, biology, chemistry, and engineering, Perseus Books,Reading, 1994.
- [41] Hilborn R., Chaos and nonlinear dynamics: An introduction forscientists and engineers, 2nd ed., Oxford University Press,Oxford, 2000.
- [42] Wiggins S., Introduction to applied nonlinear dynamicalsystems and chaos, Springer, New York, 2003.
- [43] Kolar-Anić L., Čupić Ž., Vukojević V., Anić S., Dinamikanelinearnih procesa, Fakultet za fizičku hemiju, Beograd, 2011.
- [44] Zakrzhevsky M., Кlokov A., Complete bifurcation analysis ofdriven damped pendulum systems, Est. J. Eng., 2011, 17, 76-87.
- [45] Clarke B.L., Stoichiometric network analysis of the oxalatepersulfate-silver oscillator, J. Chem. Phys., 1992, 97, 2459-2472.
- [46] Clarke B.L., Jiang W., Method for deriving Hopf and saddle-nodebifurcation hypersurfaces and application to a model of theBelousov-Zhabotinskii system, J. Chem. Phys., 1993, 99, 4464-4478.
- [47] Marković V.M., Čupić Ž., Ivanović A., Kolar-Anić L., The stabilityof the extended model of hypothalamic-pituitary-adrenal axisexamined by stoichiometric network analysis,Russ. J. Phys.Chem. A, 2011, 85, 2327-2335.
- [48] Kolar-Anić L., Čupić Ž., Anić S., Schmitz G., Pseudo-steadystates in the model of the Bray–Liebhafsky oscillatory reaction,J. Chem. Soc. Faraday T., 1997, 93, 2147-2152.
- [49] Schmitz G., Kolar-Anić L.Z., Anić S.R., Čupić Ž.D., Stoichiometricnetwork analysis and associated dimensionless kineticequations. application to a model of the Bray−Liebhafskyreaction, J. Phys. Chem. A, 2008, 112, 13452-13457.
- [50] Maćešić S., Čupić Ž., Kolar-Anić L., Model of a nonlinear reactionsystem with autocatalysis and autoinhibition: Stability ofdynamic states, Hem. Ind., 2012, 66, 637- 646.[Crossref]
- [51] Hadač O., Schreiber I., Stoichiometric network analysis of thephotochemical processes in the mesopause region, Phys.Chem. Chem. Phys., 2011, 13, 1314-1322. [Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_1515_chem-2015-0077