Geodesic
Monotonicity of the Poincar\'{e} mapping in some models of circular gene networks
Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 3, pp. 39-47

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We obtain some sufficient conditions for the existence of a periodic trajectory of the Elowitz–Leibler type piecewise linear dynamical system that simulates a simplest nonsymmetric circular gene network. We prove the monotonicity of the corresponding Poincaré mapping and construct an invariant toric neighborhood of this cycle.
Keywords: circular gene network, positive and negative feedbacks, piecewise-linear dynamical system, Poincaré mapping, cycle.
Mots-clés : invariant domain 
@article{SJIM_2019_22_3_a3,
     author = {V. P. Golubyatnikov and L. S. Minushkina},
     title = {Monotonicity of the {Poincar\'{e}} mapping in some models of circular gene networks},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {39--47},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2019_22_3_a3/}
}
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V. P. Golubyatnikov; L. S. Minushkina. Monotonicity of the Poincar\'{e} mapping in some models of circular gene networks. Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 3, pp. 39-47. http://geodesic.mathdoc.fr/item/SJIM_2019_22_3_a3/