Geodesic
On one piecewise linear dynamical system which models a gene network with variable feedback
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 4, pp. 28-37

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Discretization of phase portrait of one 3-dimensional biochemical kinetics dynamical system with piecewise linear right-hand sides of special form is constructed. We describe geometry of this phase portrait and construct there a piecewise linear invariant surface bounded by a stable cycle which is composed by eight rectilinear segments.
Keywords: gene network modeling, positive and negative feedbacks, phase portraits of dynamical systems, the Poincare map
Mots-clés : cycles, invariant surfaces, projective transformations. 
@article{VNGU_2016_16_4_a3,
     author = {V. P. Golubyatnikov and M. V. Kazantsev},
     title = {On one piecewise linear dynamical system which models a gene network with variable feedback},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {28--37},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2016_16_4_a3/}
}
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V. P. Golubyatnikov; M. V. Kazantsev. On one piecewise linear dynamical system which models a gene network with variable feedback. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 4, pp. 28-37. http://geodesic.mathdoc.fr/item/VNGU_2016_16_4_a3/