Geodesic
Mathematical Modeling of Interaction of Two Cells in the Proneural Cluster of the Wing Imaginal Disk of D. Melanogaster
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 4, pp. 3-10 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the phase portrait of a 6-dimensional nonlinear dynamical system considered as a model of an early stage of morphogenesis of D. melanogaster, i.e., appearance of its parental cell in the proneural cluster. Sufficient conditions of existence of two stable equilibrium points of this system are described, and biological interpretation is given.
Keywords: cell complex, nonlinear dynamical systems, negative and positive feedbacks, equilibrium points, the Notch signaling pathway. 
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     title = {Mathematical {Modeling} of {Interaction} of {Two} {Cells} in the {Proneural} {Cluster} of the {Wing} {Imaginal} {Disk} {of~D.~Melanogaster}},
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A. A. Akinshin; T. A. Bukharina; V. P. Golubyatnikov; D. P. Furman. Mathematical Modeling of Interaction of Two Cells in the Proneural Cluster of the Wing Imaginal Disk of D. Melanogaster. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 4, pp. 3-10. http://geodesic.mathdoc.fr/item/VNGU_2014_14_4_a0/

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