System size stochastic resonance: General nonequilibrium potential framework

Abstract

We study the phenomenon of system size stochastic resonance within the nonequilibrium potential's framework. We analyze three different cases of spatially extended systems, exploiting the knowledge of their nonequilibrium potential, showing that through the analysis of that potential we can obtain a clear physical interpretation of this phenomenon in wide classes of extended systems. Depending on the characteristics of the system, the phenomenon results to be associated to a breaking of the symmetry of the nonequilibrium potential or to a deepening of the potential minima yielding an effective scaling of the noise intensity with the system size.

Aspects of stochastic resonance in reaction–diffusion systems: The nonequilibrium-potential approach

“…It exhibits a broad resonance since for k not too large (indicating a high reflectiveness at the boundary or a reduced exchange with the environment) R increases with k, whereas it slightly decreases for larger k values (where the system's boundaries become absorbent). An explanation of this behavior in terms of the NEP has been given in [29]: as already observed, the NEP's symmetry is broken for this value of y L ; moreover, whereas the lower branch in Fig. 2b goes rapidly towards the value corresponding to Dirichlet's b.c.…”

“…The explanation offered in [27] to the phenomenon resorted to a collective variable X ≈ (1/N ) N j=1 x j , and to the fact that the noise in the effective stochastic differential equation for X scaled with size. In [29] it was shown that all the cases discussed in [27] can be put within the same NEP framework than the above studied scalar model. In fact, the aforementioned almost linear increasing dependence of ∆F 1 (y L ) on y L can be interpreted as a noise scaling with size.…”

“…There are however situations where the NEP's symmetry is retained as the system's size is varied. We may then speak of a genuinely noise-scaling SSSR, in contrast to the cases that could be called NEP symmetry breaking SSSR [29]. …”

“…Here we discuss in some detail a one-component ("scalar") RD system [21], and briefly refer to other cases analyzed in [27] and [29].…”

Collective dynamics of a network of ratchets coupled via a stochastic dynamical environment

“…This symmetry-breaking phenomenon could be associated with the breaking of the symmetry of the nonequilibrium potential given by Eq. (2) [54]. In Fig.…”