Stochastic resonance in spatially extended systems: the role of far from equilibrium potentials

Abstract

Previous works have shown numerically that the response of a "stochastic resonator" is enhanced as a consequence of spatial coupling. Also, similar results have been obtained in a reaction-diffusion model by studying the phenomenon of stochastic resonance (SR) in spatially extended systems using nonequilibrium potential (NEP) techniques. The knowledge of the NEP for such systems allows us to determine the probability for the decay of the metastable extended states, and approximate expressions for the correlation function and the signal-to-noise ratio (SNR). Here, exploiting known forms of the NEP, we have investigated the role of NEP's symmetry on SR, the enhancement of the SNR due to a selectivity of the coupling or diffusion parameter, and discussed competition between local and nonlocal (excitatory) coupling. * Member of CONICET, Argentina; Electronic Address: wio@cab.cnea.gov.ar †

System size stochastic resonance: General nonequilibrium potential framework

“…In particular we will exploit some of the results on the influence of general boundary conditions (called albedo) found in [24] as well as previous studies of the NEP [14] and of SR [6,7,8,9].…”

“…(1)) a fluctuation term, that we model as an additive noise source [9,25], yielding a stochastic partial differential equation for the random field φ(y, t)…”

“…As was discussed in [6,7,8,9], using known results for activation processes in multidimensional systems [26], we can estimate the activation rate according to the following Kramers' like result for τ , the first-passage-time for the transitions between attractors,…”

“…These were, together with the possible technological applications, the main motivation to many recent studies showing the possibility of achieving an enhancement of the system response by means of the coupling of several units in what conforms an extended medium [4,5,6,7,8,9], or analyzing the possibility of making the system response less dependent on a fine tuning of the noise intensity, as well as different ways to control the phenomenon [10,11].…”

“…In previous papers [6,7,8,9,12] we have studied the stochastic resonant phenomenon in extended systems for the transition between two different patterns, exploiting the concept of nonequilibrium potential (NEP) [13,14]. This potential is a special Lyapunov functional of the associated deterministic system which for nonequilibrium systems plays a role similar to that played by a thermodynamic potential in equilibrium thermodynamics [13].…”