This article is cited in 3 papers

On Periodic Trajectories of Nonlinear Dynamical Systems of a Special Type

V. P. Golubyatnikov^ab, I. V. Golubyatnikov<sup>a

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University

Abstract: 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, invariant domains, symbolic dynamics, cycles, transfer matrix, unimodal functions.

UDC: 514.745.82

Received: 25.04.2010