Structures of chaos in open reaction systems
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 d...istinguished. 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.
Source:
Physical Chemistry Chemical Physics, 2011, 13, 45, 20162-20171Publisher:
- Royal Soc Chemistry, Cambridge
Funding / projects:
- Dynamics of nonlinear physicochemical and biochemical systems with modeling and predicting of their behavior under nonequilibrium conditions (RS-172015)
- Nanostructured Functional and Composite Materials in Catalytic and Sorption Processes (RS-45001)
DOI: 10.1039/c1cp22496d
ISSN: 1463-9076
PubMed: 21993658
WoS: 000296871500018
Scopus: 2-s2.0-81255195879
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Institution/Community
IHTMTY - JOUR AU - Ivanović-Šašić, Ana AU - Markovic, V. M. AU - Anić, Slobodan AU - Kolar-Anić, Ljiljana AU - Čupić, Željko PY - 2011 UR - https://cer.ihtm.bg.ac.rs/handle/123456789/841 AB - 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. PB - Royal Soc Chemistry, Cambridge T2 - Physical Chemistry Chemical Physics T1 - Structures of chaos in open reaction systems VL - 13 IS - 45 SP - 20162 EP - 20171 DO - 10.1039/c1cp22496d ER -
@article{ author = "Ivanović-Šašić, Ana and Markovic, V. M. and Anić, Slobodan and Kolar-Anić, Ljiljana and Čupić, Željko", year = "2011", 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.", publisher = "Royal Soc Chemistry, Cambridge", journal = "Physical Chemistry Chemical Physics", title = "Structures of chaos in open reaction systems", volume = "13", number = "45", pages = "20162-20171", doi = "10.1039/c1cp22496d" }
Ivanović-Šašić, A., Markovic, V. M., Anić, S., Kolar-Anić, L.,& Čupić, Ž.. (2011). Structures of chaos in open reaction systems. in Physical Chemistry Chemical Physics Royal Soc Chemistry, Cambridge., 13(45), 20162-20171. https://doi.org/10.1039/c1cp22496d
Ivanović-Šašić A, Markovic VM, Anić S, Kolar-Anić L, Čupić Ž. Structures of chaos in open reaction systems. in Physical Chemistry Chemical Physics. 2011;13(45):20162-20171. doi:10.1039/c1cp22496d .
Ivanović-Šašić, Ana, Markovic, V. M., Anić, Slobodan, Kolar-Anić, Ljiljana, Čupić, Željko, "Structures of chaos in open reaction systems" in Physical Chemistry Chemical Physics, 13, no. 45 (2011):20162-20171, https://doi.org/10.1039/c1cp22496d . .