Impact Factor

    Elena Nozdrinova

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


    Pochinka O. V., Loginova A. S., Nozdrinova E. V.
    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
    Citation: Pochinka O. V., Loginova A. S., Nozdrinova E. V.,  One-Dimensional Reaction-Diffusion Equations and Simple Source-Sink Arcs on a Circle, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 3, pp.  325-330

    Back to the list