Geodesic
Structure of the phase portrait of a piecewise-linear dynamical system
Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 4, pp. 19-25

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We consider some piecewise linear $4$-dimensional dynamical system that models a gene network regulated by one negative feedback and three positive feedbacks. Glass and Pasternack described the conditions for the existence of a stable cycle in this model. We construct an invariant piecewise linear surface with nontrivial link with the Glass–Pasternack cycle outside the attraction domain of this stable cycle in the phase portrait of this system.
Keywords: block-linear dynamical systems, Poincaré mapping, gene network models, Hopf link.
Mots-clés : phase portraits, invariant surfaces, cycles 
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     title = {Structure of the phase portrait of a piecewise-linear dynamical system},
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     url = {http://geodesic.mathdoc.fr/item/SJIM_2019_22_4_a1/}
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N. B. Ayupova; V. P. Golubyatnikov. Structure of the phase portrait of a piecewise-linear dynamical system. Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 4, pp. 19-25. http://geodesic.mathdoc.fr/item/SJIM_2019_22_4_a1/