Critical properties of excitation waves on curved surfaces: Curvature-dependent loss of excitability

– In the literature, different properties of propagating excitation waves on curved surfaces are published. Theoretical papers predicted critical properties of waves on curved surfaces. If an excitation wave propagates in a non-planar system, its geodetic curvature causes a transition from excitable to non-excitable dynamics. In this paper we present first experimental results of the transition in a weakly excitable BZ system which are in good agreement with the theoretical predictions. Introduction. – Excitation wave patterns occur in many physical, chemical, and biological systems [1–3]. Up to now, most investigations were done in planar geometries. But in nature there are many two-dimensional systems which must be considered as an excitable medium with a curved surface. An important example is the heart, where the excitation waves move along the muscle in a ring-like fashion. Although during the last decade some properties of excitation fronts on curved surfaces were studied theoretically [4–6] and experimentally [7–9], there are still many gaps in our understanding of processes in non-planar systems. An important aspect, especially in biological systems, is the study of possible mechanisms for controlling these waves. Recently, new qualitative properties of excitation fronts on curved surfaces have been predicted and confirmed by computer simulations [6]. In particular, it has been shown that under certain conditions a curved surface can express critical properties, i.e., excitation fronts with sufficiently large geodetic curvature will be broken in a weakly excitable medium. Moreover, it was shown that some surfaces (for example, “bottle-like” surfaces) can act as a diode being “transparent” for wave propagation only in one direction, but not in the other. Note that the diode effect can also be observed in inhomogeneous planar excitable media [10] and in photosensitive BZ systems [11]. In this paper we describe the first experimental observations of critical properties of curved surfaces, such as breaking of wave fronts, in using a periodically curved system with a weakly excitable BZ reaction. (∗) E-mail: [email protected] (∗∗) E-mail: [email protected]