Autocatalator as the source of instability in the complex non-linear neuroendocrine model
Abstract
The mathematical analogy between properties of simple and complex models of non-linear reactions was used to determine reaction steps in the complex model, necessary to generate instability region and appropriate type of bifurcations on the border between stable and unstable non-equilibrium stationary state. The autocatalator was recognized as the simple prototype two-variable non-linear model practical for examination of the complex four-variable non-linear neuroendocrine system known as the Hypothalamic-Pituitary-Adrenal (HPA) axis. In both cases, we derived the instability criteria by stoichiometric network analysis (SNA), determine conditions under which dynamic transitions, i.e. bifurcations occur, and identify the type of bifurcation. The supercritical Andronov-Hopf bifurcation was found in both cases whereas saddle-node bifurcation was detected only in the model for HPA axis. Thus, by stoichiometric network analysis, the mathematical analogy is found between two different models... with same autocatalytic steps, that is, between two models with easily recognizable qualitative analogy.
Keywords:
Autocatalator / Hypothalamic-Pituitary-Adrenal (HPA) axis / Oscillatory reaction / Stoichiometric network analysis / Bifurcations / Non-linear dynamicsSource:
International Journal of Non-Linear Mechanics, 2015, 73, 25-30Publisher:
- Oxford : Pergamon-Elsevier Science Ltd
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: 10.1016/j.ijnonlinmec.2014.11.008
ISSN: 0020-7462
WoS: 000355022100005
Scopus: 2-s2.0-84928531278
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Institution/Community
IHTMTY - JOUR AU - Macesic, Stevan R. AU - Čupić, Željko AU - Anić, Slobodan AU - Kolar-Anić, Ljiljana PY - 2015 UR - https://cer.ihtm.bg.ac.rs/handle/123456789/1665 AB - The mathematical analogy between properties of simple and complex models of non-linear reactions was used to determine reaction steps in the complex model, necessary to generate instability region and appropriate type of bifurcations on the border between stable and unstable non-equilibrium stationary state. The autocatalator was recognized as the simple prototype two-variable non-linear model practical for examination of the complex four-variable non-linear neuroendocrine system known as the Hypothalamic-Pituitary-Adrenal (HPA) axis. In both cases, we derived the instability criteria by stoichiometric network analysis (SNA), determine conditions under which dynamic transitions, i.e. bifurcations occur, and identify the type of bifurcation. The supercritical Andronov-Hopf bifurcation was found in both cases whereas saddle-node bifurcation was detected only in the model for HPA axis. Thus, by stoichiometric network analysis, the mathematical analogy is found between two different models with same autocatalytic steps, that is, between two models with easily recognizable qualitative analogy. PB - Oxford : Pergamon-Elsevier Science Ltd T2 - International Journal of Non-Linear Mechanics T1 - Autocatalator as the source of instability in the complex non-linear neuroendocrine model VL - 73 SP - 25 EP - 30 DO - 10.1016/j.ijnonlinmec.2014.11.008 ER -
@article{ author = "Macesic, Stevan R. and Čupić, Željko and Anić, Slobodan and Kolar-Anić, Ljiljana", year = "2015", abstract = "The mathematical analogy between properties of simple and complex models of non-linear reactions was used to determine reaction steps in the complex model, necessary to generate instability region and appropriate type of bifurcations on the border between stable and unstable non-equilibrium stationary state. The autocatalator was recognized as the simple prototype two-variable non-linear model practical for examination of the complex four-variable non-linear neuroendocrine system known as the Hypothalamic-Pituitary-Adrenal (HPA) axis. In both cases, we derived the instability criteria by stoichiometric network analysis (SNA), determine conditions under which dynamic transitions, i.e. bifurcations occur, and identify the type of bifurcation. The supercritical Andronov-Hopf bifurcation was found in both cases whereas saddle-node bifurcation was detected only in the model for HPA axis. Thus, by stoichiometric network analysis, the mathematical analogy is found between two different models with same autocatalytic steps, that is, between two models with easily recognizable qualitative analogy.", publisher = "Oxford : Pergamon-Elsevier Science Ltd", journal = "International Journal of Non-Linear Mechanics", title = "Autocatalator as the source of instability in the complex non-linear neuroendocrine model", volume = "73", pages = "25-30", doi = "10.1016/j.ijnonlinmec.2014.11.008" }
Macesic, S. R., Čupić, Ž., Anić, S.,& Kolar-Anić, L.. (2015). Autocatalator as the source of instability in the complex non-linear neuroendocrine model. in International Journal of Non-Linear Mechanics Oxford : Pergamon-Elsevier Science Ltd., 73, 25-30. https://doi.org/10.1016/j.ijnonlinmec.2014.11.008
Macesic SR, Čupić Ž, Anić S, Kolar-Anić L. Autocatalator as the source of instability in the complex non-linear neuroendocrine model. in International Journal of Non-Linear Mechanics. 2015;73:25-30. doi:10.1016/j.ijnonlinmec.2014.11.008 .
Macesic, Stevan R., Čupić, Željko, Anić, Slobodan, Kolar-Anić, Ljiljana, "Autocatalator as the source of instability in the complex non-linear neuroendocrine model" in International Journal of Non-Linear Mechanics, 73 (2015):25-30, https://doi.org/10.1016/j.ijnonlinmec.2014.11.008 . .