Dispersion Curves and Pulse Wave Propagation in Excitable Systems

Abstract

The excitation and wave propagation phenomena are common in systems of varying nature such as plasmas, excitable tissues in living organisms, heterogeneous catalytic reactions, combustion, homogeneous autocatalytic reactions, populations of living organisms and so on /1,2/. Results of empirical observations, planned experiments and mathematical modelling have accumulated in recent years but comparisons and generalizations valid for common phenomena in different systems are scarce. Here we attempt to briefly compare generation and propagation of action potential in nerve tissue and initiation and propagation of concentration waves in chemical reaction-diffusion systems. We use experimental facts well known from the studies of receptors and propagation of the action potential in nerve fibers /3,4,5/ and modelling results for the processes of nerve conduction /6,7,8,9/ on one hand and the results of experimental and modelling studies of pulse wave initiation and propagation in spatially quasi one- and two- dimensional reaction-diffusion systems on the other hand. Experimental systems quoted here are represented by a thin layer of reacting mixture of the Belousov-Zhabotinski (B-Z) type /10/; either kinetic model of the B-Z reaction (Oregonator /11,12,13/) or kinetic SH model /14,15/ were considered.KeywordsDispersion RelationWave TrainWave PatternExcitable MediumSpiral WaveThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.