This article is cited in 2 papers

On structure of phase portraits of some nonlinear dynamical systems

V. P. Golubyatnikov^ab, A. E. Kalenykh<sup>b

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

Abstract: We study phase portrait of one piece-wise linear dynamical system of chemical kinetics. Earlier L. Glass and J. Pasternack have obtained conditions of existence of a stable cycle of this system. We construct here an invariant piece-wise linear surface which consists of trajectories of this system and is disjoined with the attraction basin of that stable cycle. We prove that this surface does not contain cycles of this dynamical system.

Keywords: dynamical systems, phase portraits, oscillating trajectories, invariant surfaces.

UDC: 514.745.82

Received: 19.01.2015

 English version: Journal of Mathematical Sciences, 2016, 215:4, 475–483