Geodesic
Cycles in the odd-dimensional models of circular gene networks
Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 4, pp. 28-38

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The necessary and sufficient conditions are obtained for the existence of a cycle in an odd-dimensional nonlinear dynamical system that simulates the functioning of the simplest circular gene network. An invariant neighborhood of this cycle is described which is homeomorphic to a torus.
Keywords: block-linear autonomous system, circular gene network, fixed point of a monotonic mapping, cycle.
Mots-clés : phase portrait 
@article{SJIM_2018_21_4_a2,
     author = {V. P. Golubyatnikov and V. V. Ivanov},
     title = {Cycles in the odd-dimensional models of circular gene networks},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {28--38},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2018_21_4_a2/}
}
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V. P. Golubyatnikov; V. V. Ivanov. Cycles in the odd-dimensional models of circular gene networks. Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 4, pp. 28-38. http://geodesic.mathdoc.fr/item/SJIM_2018_21_4_a2/