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About distributed control in model of testosterone regulation

In: Tatra Mountains Mathematical Publications, vol. 71, no. 1
Olga Pinhasov
Detaily:
Rok, strany: 2019, 149 - 154
Jazyk: eng
Kľúčové slová:
integro-differential equations, stability, reduction method, testosterone regulation
Typ článku: Mathematics
O článku:
In the paper, stability of integro-differential equation is studied. The model of testosterone regulation is considered. The model describes an interaction of: the concentration of hormone (GnRH) which will be denoted as $x_{1}$, with the concentration of the hormone (LH)-$x_{2}$ and the concentration of testosterone (Te)-$x_{3}$ and can be written in the form \begin{equation*} \begin{array}{l} \displaystyle\left\{ \begin{array}{l} \displaystyle x_{1}^{\prime }(t)+b_{1}x_{1}(t)=0, \\ \displaystyle x_{2}^{\prime }(t)+b_{2}x_{2}(t)-g_{1}x_{1}(t)=0, \\ \displaystyle x_{3}^{\prime }(t)+b_{3}x_{3}(t)-c_{1}\int\limits_{0}^{t} e^{-\alpha _{1}(t-s)}x_{2}(s) \, ds=0, \quad t\geq 0.% \end{array} \right. \end{array} \end{equation*} The values $b_{i}$, $i=1,2,3$ correspond to the respective half-life times of {GnRH}, {LH} and {Te}. The aim of the work is to propose a concept to hold the concentration of testosterone above a corresponding level. In order to achieve this, distributed input control in the form of integral term is used.
Ako citovať:
ISO 690:
Pinhasov, O. 2019. About distributed control in model of testosterone regulation. In Tatra Mountains Mathematical Publications, vol. 71, no.1, pp. 149-154. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2018-0013

APA:
Pinhasov, O. (2019). About distributed control in model of testosterone regulation. Tatra Mountains Mathematical Publications, 71(1), 149-154. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2018-0013
O vydaní:
Vydavateľ: MÚ SAV
Publikované: 2. 1. 2019