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Autocatalator as the source of instability in the complex non-linear neuroendocrine model

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2015
Authors
Macesic, Stevan R.
Čupić, Željko
Anić, Slobodan
Kolar-Anić, Ljiljana
Article (Published version)
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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 dynamics
Source:
International Journal of Non-Linear Mechanics, 2015, 73, 25-30
Publisher:
  • Pergamon-Elsevier Science Ltd, Oxford
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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URI
http://cer.ihtm.bg.ac.rs/handle/123456789/1665
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