Optimal range of a nonlocal kernel for stochastic resonance in extended systems

Here we study stochastic resonance (SR) in a spatially extended system described by a reaction–diffusion equation for a scalar (activator-like) field including a nonlocal contribution. We assume that such a contribution arises from an effective adiabatic elimination of an auxiliary (inhibitor-like) field. Our aim is to study the role played by the range of the nonlocal kernel on the SR phenomena. We have found that increasing the nonlocal coupling reduces the systemʹs response and that, similar to the so-called system size SR, there is an “optimal” value of the kernelʹs range, yielding a maximum in the systemʹs response.