Stoichiometric network analysis as mathematical method for examinations of instability region and oscillatory dynamics
Apstrakt
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.
Ključne reči:
Stoichiometric network analysis (SNA) / mathematical modeling / stoichiometric models / nonlinear oscillatory reaction system / instability conditionIzvor:
Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informa, 2016, 8, 1, 43-64Izdavač:
- Državni univerzitet, Novi Pazar
Institucija/grupa
IHTMTY - JOUR AU - Čupić, Željko AU - Schmitz, G. AU - Kolar-Anić, Ljiljana PY - 2016 UR - https://cer.ihtm.bg.ac.rs/handle/123456789/2030 AB - 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. PB - Državni univerzitet, Novi Pazar T2 - Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informa T1 - Stoichiometric network analysis as mathematical method for examinations of instability region and oscillatory dynamics VL - 8 IS - 1 SP - 43 EP - 64 DO - 10.5937/SPSUNP1601043C ER -
@article{ author = "Čupić, Željko and Schmitz, G. and Kolar-Anić, Ljiljana", year = "2016", abstract = "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.", publisher = "Državni univerzitet, Novi Pazar", journal = "Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informa", title = "Stoichiometric network analysis as mathematical method for examinations of instability region and oscillatory dynamics", volume = "8", number = "1", pages = "43-64", doi = "10.5937/SPSUNP1601043C" }
Čupić, Ž., Schmitz, G.,& Kolar-Anić, L.. (2016). Stoichiometric network analysis as mathematical method for examinations of instability region and oscillatory dynamics. in Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informa Državni univerzitet, Novi Pazar., 8(1), 43-64. https://doi.org/10.5937/SPSUNP1601043C
Čupić Ž, Schmitz G, Kolar-Anić L. Stoichiometric network analysis as mathematical method for examinations of instability region and oscillatory dynamics. in Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informa. 2016;8(1):43-64. doi:10.5937/SPSUNP1601043C .
Čupić, Željko, Schmitz, G., Kolar-Anić, Ljiljana, "Stoichiometric network analysis as mathematical method for examinations of instability region and oscillatory dynamics" in Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informa, 8, no. 1 (2016):43-64, https://doi.org/10.5937/SPSUNP1601043C . .