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