Spatial decoherence induced by small-world connectivity in excitable media

We study effects of different network topologies on the noise-induced pattern formation in a two-dimensional model of excitable media with FitzHugh-Nagumo local dynamics. In particular, we show that the introduction of long-range couplings induces decoherence of otherwise coherent noise-induced spatial patterns that can be observed by regular connectivity of spatial units. Importantly, already a small fraction of long-range couplings is sufficient to destroy coherent pattern formation. We argue that the small-world network topology destroys spatial order due to the lack of a precise internal spatial scale, which by regular connectivity is given by the coupling constant and the noise robust excursion time that is characteristic for the local dynamics. Additionally, the importance of spatially versus temporally ordered neural network functioning is discussed