AbstractIn 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, \\[1.0ex] \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, ~~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\abbr{GnRH}, \abbr{LH} and \abbr{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.
@article{526,
title = {About distributed control in model of testosterone regulation},
journal = {Tatra Mountains Mathematical Publications},
volume = {72},
year = {2019},
language = {EN},
url = {http://dml.mathdoc.fr/item/526}
}
Pinhasov, Olga. About distributed control in model of testosterone regulation. Tatra Mountains Mathematical Publications, Tome 72 (2019) . http://gdmltest.u-ga.fr/item/526/