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Negrojević L, Lončar A, Maksimović J, Anić S, Čupić Ž, Kolar-Anić L, Pejić N. Bray–Liebhafsky oscillatory reaction in a continuous-flow stirred tank reactor as the matrix system for determination of tyrosine. REACTION KINETICS MECHANISMS AND CATALYSIS 2022. [DOI: 10.1007/s11144-021-02130-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/07/2022]
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Anić SR, Čupić ŽD. Dynamics and kinetics of complex reaction systems. Contributions of the Professor emeritus Ljiljana Kolar-Anić. REACTION KINETICS MECHANISMS AND CATALYSIS 2018. [DOI: 10.1007/s11144-017-1290-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Bifurcation analysis: a tool for determining model parameters of the considered process. REACTION KINETICS MECHANISMS AND CATALYSIS 2017. [DOI: 10.1007/s11144-017-1324-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Schmitz G. Historical overview of the oscillating reactions. Contribution of Professor Slobodan Anić. REACTION KINETICS MECHANISMS AND CATALYSIS 2016. [DOI: 10.1007/s11144-015-0968-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Bubanja IN, Maćešić S, Ivanović-Šašić A, Čupić Ž, Anić S, Kolar-Anić L. Intermittent chaos in the Bray-Liebhafsky oscillator. Temperature dependence. Phys Chem Chem Phys 2016; 18:9770-8. [PMID: 27001164 DOI: 10.1039/c6cp00759g] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Intermittent oscillations as a chaotic mixture of large amplitude relaxation oscillations, grouped in bursts and small-amplitude sinusoidal ones or even quiescent parts between them known as gaps, were found and examined in the Bray-Liebhafsky (BL) reaction performed in CSTR under controlled temperature variations. They were obtained in a narrow temperature range from 61.0 °C to 63.1 °C, where 61.0 °C is the critical temperature for burst emergence from the stable steady state and 63.1 °C is the critical temperature for gap emergence from regular oscillations. Since intermittencies appear gradually from the regular oscillatory state, and no hysteresis was obtained with decreasing/increasing temperature in the vicinity of these two bifurcations, a linear relationship between (τB/τ)(2) and (τG/τ)(2) (where τB, τG and τ denotes duration of bursts, gaps, and whole experiment, respectively), as a function of the temperature as the control parameter, was expected and obtained. Although these intermittent oscillations are chaotic with respect to the lengths of individual gaps as well as bursts, their deterministic behavior related to temperature was additionally established. Thus, the number of bursts or gaps per unit of time (NB/τ and NG/τ) has the form of a normal distribution function over the temperature range in the region where intermittencies are obtained. Temperature dependence of the Lyapunov exponents was also described by a function of the normal distribution form. Hence, we established some regularities in the chaotic behavior of intermittent oscillations that are common in life but difficult for determinations.
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Affiliation(s)
- I N Bubanja
- Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12 - 16, RS-11000 Belgrade.
| | - S Maćešić
- Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12 - 16, RS-11000 Belgrade.
| | - A Ivanović-Šašić
- Institute of Chemistry, Technology and Metallurgy, Center of Catalysis and Chemical Engineering, University of Belgrade, Njegoševa 12, RS-11000 Belgrade
| | - Ž Čupić
- Institute of Chemistry, Technology and Metallurgy, Center of Catalysis and Chemical Engineering, University of Belgrade, Njegoševa 12, RS-11000 Belgrade
| | - S Anić
- Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12 - 16, RS-11000 Belgrade. and Institute of Chemistry, Technology and Metallurgy, Center of Catalysis and Chemical Engineering, University of Belgrade, Njegoševa 12, RS-11000 Belgrade
| | - Lj Kolar-Anić
- Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12 - 16, RS-11000 Belgrade. and Institute of Chemistry, Technology and Metallurgy, Center of Catalysis and Chemical Engineering, University of Belgrade, Njegoševa 12, RS-11000 Belgrade
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Bifurcation analysis of the reduced model of the Bray–Liebhafsky reaction. REACTION KINETICS MECHANISMS AND CATALYSIS 2016. [DOI: 10.1007/s11144-016-1000-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Pejić N, Kolar-Anić L, Maksimović J, Janković M, Vukojević V, Anić S. Dynamic transitions in the Bray–Liebhafsky oscillating reaction. Effect of hydrogen peroxide and temperature on bifurcation. REACTION KINETICS MECHANISMS AND CATALYSIS 2016. [DOI: 10.1007/s11144-016-0984-y] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Pejić N, Vujković M, Maksimović J, Ivanović A, Anić S, Čupić Ž, Kolar-Anić L. Dynamic behavior of the bray-liebhafsky oscillatory reaction controlled by sulfuric acid and temperature. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A 2011. [DOI: 10.1134/s0036024411130231] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Marković VM, Čupić Ž, Ivanović A, Kolar-Anić L. The stability of the extended model of hypothalamic-pituitary-adrenal axis examined by stoichiometric network analysis. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A 2011. [DOI: 10.1134/s0036024411130115] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Ivanović-Šašić AZ, Marković VM, Anić SR, Kolar-Anić LZ, Cupić ŽD. Structures of chaos in open reaction systems. Phys Chem Chem Phys 2011; 13:20162-71. [PMID: 21993658 DOI: 10.1039/c1cp22496d] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
By numerically simulating the Bray-Liebhafsky (BL) reaction (the hydrogen peroxide decomposition in the presence of hydrogen and iodate ions) in a continuously fed well stirred tank reactor (CSTR), we find "structured" types of chaos emerging in regular order with respect to flow rate as the control parameter. These chaotic "structures" appear between each two successive periodic states, and have forms and evolution resembling to the neighboring periodic dynamics. More precisely, in the transition from period-doubling route to chaos to the arising periodic mixture of different mixed-mode oscillations, we are able to recognize and qualitatively and quantitatively distinguish the sequence of "period-doubling" chaos and chaos consisted of mixed-mode oscillations (the "mixed-mode structured" chaos), both appearing in regular order between succeeding periodic states. Additionally, between these types of chaos, the chaos without such recognizable "structures" ("unstructured" chaos) is also distinguished. Furthermore, all transitions between two successive periodic states are realized through bifurcation of chaotic states. This scenario is a universal feature throughout the whole mixed-mode region, as well as throughout other mixed-mode regions obtained under different initial conditions.
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Affiliation(s)
- A Z Ivanović-Šašić
- Institute of Chemistry, Technology and Metallurgy, University of Belgrade, Department of Catalysis and Chemical Engineering, Njegoševa 12, Belgrade, Serbia
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