The Interaction of Belousov-Zhabotinsky Travelling Waves across a Semi-Permeable Membrane

M. J. Metcalf¹, J. H. Merkin² and S. K. Scott³

¹Kyoto Institute of Technology, Matsugasaki, Sakyo, Kyoto 606, Japan
²Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, U.K.
³School of Chemistry, University of Leeds, Leeds, LS2 9JT, U.K.

(Received March 30, 1995; Accepted December 20, 1995)

Keywords: Coupled Waves, Excitable System, BZ Waves

Abstract. The propagation of Belousov-Zhabotinsky waves in two parallel regions, coupled together by a linear diffusive interchange of the autocatalytic species across a semi-permeable membrane is considered. The spatiotemporal patterns that develop are analysed in terms of two parameters that arise, namely the coupling strength and the distance between waves at which coupling first begins. It is found that there is a critical point where two passing waves will not interact until their wave-backs are sufficiently non-refractory. This simple configuration is shown to exhibit self-organization and self-initiation of propagating chemical waves.