Geodesic
On structure of phase portraits of some nonlinear dynamical systems
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 15 (2015) no. 1, pp. 45-53

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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, oscillating trajectories
Mots-clés : phase portraits, invariant surfaces. 
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     author = {V. P. Golubyatnikov and A. E. Kalenykh},
     title = {On structure of phase portraits of some nonlinear dynamical systems},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {45--53},
     publisher = {mathdoc},
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     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2015_15_1_a3/}
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V. P. Golubyatnikov; A. E. Kalenykh. On structure of phase portraits of some nonlinear dynamical systems. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 15 (2015) no. 1, pp. 45-53. http://geodesic.mathdoc.fr/item/VNGU_2015_15_1_a3/