Abstract.
We study the propagation of periodic pulse trains in excitable media exposed to external spatio-temporal noise using the light-sensitive Belousov-Zhabotinsky reaction with the underlying Oregonator model as representative example. In the weak noise approximation we find noise-induced transitions in the dispersion relation of pulse trains. We discuss noise-enhanced propagation of pulse trains within a certain wave-length range caused by external noise of moderate strength.
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The data presented in this figure, as all the data reported in Figures 1 and 4 and in Section 3, are obtained with the continuation software AUTO. Here the wavelenght is equivalent to the domain size L of the medium in the case of direct numerical simulations under the assumption of periodic boundary conditions
Such a correlation function is obtained numerically by dividing the spatial domain of size L into m cells of equal size l = L/m = nΔx, where Δx is the lattice spacing equal to L/N. In each cell φ fluctuates homogeneously according to φ(x,t)=φ0[1+ηi(t)] for il≤x<(i+1)l, where the stochastic variable ηi is a temporally exponentially correlated stochastic process. The correlation length is in this case \(\lambda=\frac{n}{3}\Delta x\)
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Beato, V., Engel, H. & Schimansky-Geier, L. Pulse trains propagating through excitable media subjected to external noise. Eur. Phys. J. B 58, 323–329 (2007). https://doi.org/10.1140/epjb/e2007-00228-x
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DOI: https://doi.org/10.1140/epjb/e2007-00228-x