Geodesic
Gompertz function in the model of gene regulatory networks
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 88-96

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We examine a network model (including gene regulatory networks), which consists of a system of two ordinary differential equations. This system contains several parameters and depends on the regulatory matrix, which describes interactions in this two-component network. We consider attracting sets of the system, which vary depending on the parameters and elements of the regulatory matrix. Our considerations are of geometric nature, which allows us to identify and classify possible interactions in the network. The system of differential equations contains a sigmoidal function, which makes it possible to take into account peculiarities of the network's response to external influences. The Gompertz function was chosen as the sigmoidal function, which allows us to compare the results with similar results for models of two-component networks based on the logistic sigmoidal function.
Keywords: gene regulatory network, qualitative analysis, numerical analysis.
Mots-clés : phase portrait 
@article{INTO_2021_195_a10,
     author = {D. A. Ogorelova and F. Zh. Sadyrbaev},
     title = {Gompertz function in the model of gene regulatory networks},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {88--96},
     publisher = {mathdoc},
     volume = {195},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_195_a10/}
}
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D. A. Ogorelova; F. Zh. Sadyrbaev. Gompertz function in the model of gene regulatory networks. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 88-96. http://geodesic.mathdoc.fr/item/INTO_2021_195_a10/