One-Dimensional Reaction-Diffusion Equations and Simple Source-Sink Arcs on a Circle
Received 30 May 2018; accepted 22 June 2018
2018, Vol. 14, no. 3, pp. 325-330
Author(s): 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.
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