Noise as control parameter in networks of excitable media: Role of the network topology.

We analyze coupled FitzHugh-Nagumo oscillators on various network topologies, in particular random diluted and scale-free topologies, under the influence of noise. Similarly to globally coupled excitable units, noise acts as control parameter: changing monotonically its strength, the collective dynamical behavior varies from stable equilibrium solutions to coherent firing of a large fraction, and for even stronger noise to incoherent firing leading to chaotic behavior of the excitable elements. For strong noise the system is less sensitive to the network topology. The specific topology enters via the degree of nodes and determines the average number of spikes. Apart from bifurcation regions, it is the ratio of noise intensity to size that determines the dynamical behavior of average values. Specific behavior such as limit cycles may then be realized for strong noise and large systems or for low noise and small systems. Within bifurcation regions, the actual values of noise intensity and system-size matter independently. Here we analyze in more detail phase portraits of small systems. For a given noise intensity and network topology we have studied the regularity of signals as a function of time. We observe the phenomenon of system-size resonance for a whole interval of noise intensities as long as the degree distribution is homogeneous, so that no fine tuning of the noise is needed. Therefore it is plausible that natural systems make actually use of noise when noise is unavoidably present.