Finite size effects in noise driven systems: From neural systems to fashion spreading

In the last two decades it has been adviced the non-trivial role that noise can play in non-linear systems. Among the most interesting results there are found Stochastic Resonance and Coherence Resonance. Both, show the ordering effect in the dynamics of the system of an external noise. However, very little has been studied on the effect that system size has in such systems.

First, it will be shown that for a finite-size coupled FitzHugh-Nagumo system a phenomenon called system-size coherence resonance
exists. This is, for each noise intensity exists a system size for which
the global dynamics show an optimal ordering.


Second, it will be shown the results concerning a Fashion spreading model [M. Kuperman, D. Zanette, Eur. Phys. Jour. B, 26 387 (2002)]. In this model, there is not directed opinion changing -as in voter’s model-, but a certain degree of randomness in the opinion taken by an individual. For such a model, a fashion trend is more efficiently spread in a society when a certain amount of randomness is present in the opinion taking. It will be shown in this seminar that this model also implies that there exists an optimal society size for which a fashion is most followed by the individuals.