Geodesic
On Some Nonlinear Dynamical Systems Modeling Asymmetric Gene Networks. Part~2
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 1, pp. 18-28

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We find conditions of existence of periodic trajectories for 3-dimensional nonlinear dynamical systems modeling gene networks regulated by negative feedbacks and by combinations of positive and negative feedbacks described by unimodal functions. For these dynamical systems, we obtain also sufficient conditions of existence of stable cycles and describe the topological indices of their stationary points.
Keywords: periodic trajectories, models of gene networks, positive and negative feedbacks.
Mots-clés : stable cycles 
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     title = {On {Some} {Nonlinear} {Dynamical} {Systems} {Modeling} {Asymmetric} {Gene} {Networks.} {Part~2}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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     publisher = {mathdoc},
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V. P. Golubyatnikov; Yu. A. Gaidov; V. A. Likhoshvay. On Some Nonlinear Dynamical Systems Modeling Asymmetric Gene Networks. Part~2. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 1, pp. 18-28. http://geodesic.mathdoc.fr/item/VNGU_2010_10_1_a1/