Geodesic
Phase portraits of two nonlinear models of circular gene networks
Matematičeskie zametki SVFU, Tome 30 (2023) no. 2, pp. 3-13 Cet article a éte moissonné depuis la source Math-Net.Ru

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For two dynamical systems of dimensions 4 and 5 which simulate circular gene networks with non-linear degradation of their components we find conditions for existence of periodic trajectories and construct invariant domains which contain all these trajectories. Interiors of both domains are homeomorphic to torus, and the boundary of each of them contains a unique equilibrium point of the corresponding dynamical system.
Keywords: circular gene network model, phase portrait of non-linear dynamical system, equilibrium point, periodic trajectory.
Mots-clés : invariant domain 
@article{SVFU_2023_30_2_a0,
     author = {N. B. Ayupova and V. P. Golubyatnikov},
     title = {Phase portraits of two nonlinear models of circular gene networks},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {3--13},
     year = {2023},
     volume = {30},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2023_30_2_a0/}
}
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N. B. Ayupova; V. P. Golubyatnikov. Phase portraits of two nonlinear models of circular gene networks. Matematičeskie zametki SVFU, Tome 30 (2023) no. 2, pp. 3-13. http://geodesic.mathdoc.fr/item/SVFU_2023_30_2_a0/