Geodesic
Study of a~one-dimensional model, accounting for cell division, of regulation of the renewing zone size in a~biological tissue
Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 4, pp. 70-82

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We describe the modeling of the dynamics of renewing zone structure in biological tissues in the formalism of parameterized $L$-systems on an example of the shoot apical meristem. Under study is the influence of the ratio of the characteristic times of the cell cycle and diffusion of morphogens on the stability of some spatially distributed molecular-genetic control system. We show that cell division is a perturbing factor for the system regulating the renewing zone structure. Some conditions are found for the loss of stability of the regulation.
Keywords: mathematical modeling, dynamical systems with dynamical structure, parameterized $L$-systems, shoot apical meristem, molecular-genetic control system.
Mots-clés : cell division 
@article{SJIM_2010_13_4_a6,
     author = {S. N. Nikolaev and U. S. Zubairova and S. I. Fadeev and E. Mjolsness and N. A. Kolchanov},
     title = {Study of a~one-dimensional model, accounting for cell division, of regulation of the renewing zone size in a~biological tissue},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {70--82},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2010_13_4_a6/}
}
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S. N. Nikolaev; U. S. Zubairova; S. I. Fadeev; E. Mjolsness; N. A. Kolchanov. Study of a~one-dimensional model, accounting for cell division, of regulation of the renewing zone size in a~biological tissue. Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 4, pp. 70-82. http://geodesic.mathdoc.fr/item/SJIM_2010_13_4_a6/