Geodesic
On Periodic Trajectories of Nonlinear Dynamical Systems of a Special Type
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 3, pp. 3-16

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We prove a theorem on existence of cycles in phase portraits of odd-dimensional dynamical systems modeling functioning of gene networks regulated by negative feedbacks. We find sufficient conditions of existence of stable cycles there and describe some extensions of these results to other classes of the gene networks models.
Keywords: nonlinear dynamical systems, feedbacks, stationary points, symbolic dynamics, unimodal functions.
Mots-clés : invariant domains, cycles, transfer matrix 
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     title = {On {Periodic} {Trajectories} of {Nonlinear} {Dynamical} {Systems} of a {Special} {Type}},
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V. P. Golubyatnikov; I. V. Golubyatnikov. On Periodic Trajectories of Nonlinear Dynamical Systems of a Special Type. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 3, pp. 3-16. http://geodesic.mathdoc.fr/item/VNGU_2010_10_3_a0/