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 Nelin. Dinam., 2018, Volume 14, Number 3, Pages 325–330 (Mi nd615)

One-Dimensional Reaction-Diffusion Equations and Simple Source-Sink Arcs on a Circle

O. V. Pochinka, A. S. Loginova, E. V. Nozdrinova

National Research University Higher School of Economics (HSE), ul. B. Pecherskaya 25/12, Nizhny Novgorod, 603150, Russia

Abstract: This article presents a number of models that arise in physics, biology, chemistry, etc., described by a one-dimensional reaction-diffusion equation. The local dynamics of such models for various values of the parameters is described by a rough transformation of the circle. Accordingly, the control of such dynamics reduces to the consideration of a continuous family of maps of the circle. In this connection, the question of the possibility of joining two maps of the circle by an arc without bifurcation points naturally arises. In this paper it is shown that any orientation-preserving source-sink diffeomorphism on a circle is joined by such an arc. Note that such a result is not true for multidimensional spheres.

Keywords: reaction-diffusion equation, source-sink arc

 Funding Agency Grant Number Russian Foundation for Basic Research 18-31-00022 HSE Basic Research Program This study was carried out within the framework of the RFBR project 18-31-00022 and the Basic Research Program at the National Research University Higher School of Economics (HSE) in 2018.

DOI: https://doi.org/10.20537/nd180303

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Document Type: Article
MSC: 37D15
Language: English

Citation: O. V. Pochinka, A. S. Loginova, E. V. Nozdrinova, “One-Dimensional Reaction-Diffusion Equations and Simple Source-Sink Arcs on a Circle”, Nelin. Dinam., 14:3 (2018), 325–330

Citation in format AMSBIB
\Bibitem{PocLogNoz18} \by O. V. Pochinka, A. S. Loginova, E. V. Nozdrinova \paper One-Dimensional Reaction-Diffusion Equations and Simple Source-Sink Arcs on a Circle \jour Nelin. Dinam. \yr 2018 \vol 14 \issue 3 \pages 325--330 \mathnet{http://mi.mathnet.ru/nd615} \crossref{https://doi.org/10.20537/nd180303}