Ressonância estocástica induzida por ruído não gaussiano em um modelo para a dinâmica do neurônio

Abstract

Non linear dynamical systems can present a diversity of unconventional features when perturbed by an external noise, such as an enhancing of transport properties, stabilization of spatial patterns and noise induced phase transitions. In particular, the external noise can improve the system s response to weak external periodic pulses, a phenomenon termed as stochastic resonance due to its similarity with the resonance phenomena displayed by deterministic dynamical systems. Stochastic resonance ideas have been widely applied to better understand the behavior of many physical, chemical and biological systems, such as optical, electronic and magnetic systems, chemical reactions, as well as several features regarding neuro-physiological aspects of sensory systems. In this work, we study the stochastic resonance phenomenon in the integrate-fire model for the neuronal response by a sub-threshold periodic signal. In the traditional approach the threshold level is reached by superposing a gaussian noise to the periodic drive. As non gaussian noises have been shown to be quite overspread in natural systems, we investigate the sensitivity of the stochastic resonance condition upon the noise s probability distribution function. To generate a power-law distributed noise, we considered a stochastic process with both additive and multiplicative noises which allows for a fine tuning of the asymptotic power-law decay exponent. We employed both analogical and computational solutions of the stochastic differential equations which produced similar results. The dependence of the optimal noise intensity for the stochastic resonance condition on the power-law exponent of the non gaussian noise is reported. Our main finding is that the stochastic resonance condition is achieved with a minimum intensity of the input noise when it has a probability distribution with a finite decay exponent. Therefore, neural systems can explore the non gaussian character of the input noise to improve the ability to identify sub-threshold signals. Instituto de F´ısica - UFAL