Sistemas dinâmicos excitáveis sob a ação de ruídos não-gaussianos

Abstract

Physical systems far from thermo dynamic equilibrium present excitability and irreversibility. The excitability is responsible for the great sensitivity of these systems to external stimuli while the irreversibility is associated with energy dissipation. The thermal fluctuations, inevitable in any real system, arise due to the interaction between many particles of the system. For such systems one of the best approaches is given by the non-equilibrium Statistical Mechanics, since it is virtually impossible an individualized approach of the motion equations. Many works in the current literature use a Gaussian stochastic modeling (without correlations) to represent the fluctuations. However, there is a growing number of studies reporting the occurrence of correlated fluctuations, mainly related to biological systems. In this thesis we investigate the influence of non-Gaussian stochastic distribution on the properties for two representative excitable models. In the first model we study the influence of distribution on the neural dynamics through the stochastic resonance (SR) mechanism. In the second model we approach the ratchet effect (RE) on directed transport of particles. In both systems we use a non-Gaussian power-law distributed noise obtained through a random multiplicative process (RMP). This process allows a fine tuning of the asymptotic power-law decay exponent. The optimization conditions are reported. In particular, we show that the optimization conditions for resonance and directed transport in Brownian ratchets are reached for a finit decay exponent of the stochastic distribution that represents a Strong non-Gaussian character. As non-Gaussian fluctuations occur with great frequency in natural systems, we believe that the non-Gaussian character can optimize the efficiency on the stochastic transport mechanisms in micro and nanoscale.