Stochastic resonance in extended bistable systems: The role of potential symmetry

Abstract

We study the role of potential symmetry in a three-field reaction-diffusion system presenting bistability by means of a two-state theory for stochastic resonance in general asymmetric systems. By analyzing the influence of different parameters in the optimization of the signal-to-noise ratio, we observe that this magnitude always increases with the symmetry of the system's potential, indicating that it is this feature which governs the optimization of the system's response to periodic signals.

System size stochastic resonance: General nonequilibrium potential framework

“…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,…”

“…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].…”

“…As was done in [6], we assume now that the system is (adiabatically) subject to an external harmonic variation of the parameter φ c : φ c (t) = φ * c + δφ c cos(ωt) [7,9], and exploit the "twostate approximation" [1] as in [7,8,9]. Such an approximation basically consist in reducing the whole dynamics on the bistable potential landscape to a one where the transitions occurs between two states: the ones associated to the bottom of each well, while the dynamics is contained only in the transition rates.…”

“…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].…”