On the Role of Non-Gaussian Noises on Noise-Induced Phenomena

Abstract

Most of the studies of noise-induced phenomena assume that the noise source is Gaussian (either white or colored). Here we present recent results of some of those noise-induced phenomena when driven by a noise source taken as colored and non-Gaussian, generated by a nonextensive g-distribution. In all the cases analyzed we have found that the response of the system is strongly affected by a departure of the noise source from the Gaussian behavior, showing an enhancement and/or a marked broadening of the corresponding system's response. The general result is that the value of the parameter q, optimizing the system's response, results in q ≠ 1 (where q = 1 corresponds to a Gaussian distribution). These results are of great relevance for many technological applications as well as for some situations of medical interest, like the noisy control of Wenckebach rhythms…. Fluctuations (or noise) have had a changing role in the history of science. We can identify three different stages. During the a first one, which lasted until the end of nineteenth century, noise was considered a nuisance to be avoided or eliminated. In the second stage, which started at the beginning of the twentieth century, it was possible to extract more information from a physical system through the study of fluctuations via Onsager, fluctuation-dissipation, and other related relations. The third stage corresponds to the last few decades of the twentieth century, with the recognition that in many situations noise can actually play a driving role that induces new phenomena. Some examples are noise-induced phase transitions [18, 27, 28], noise-induced transport [2, 29, 34, 35], stochastic resonance [17], and noise-sustained patterns [18]. Most of the studies on the noise-induced phenomena indicated above assume that the noise source is Gaussian (either white or colored). In addition to the intrinsic interest in the study of non-Gaussian noises, there is some experimental evidence, particularly in sensory and biological systems [3, 16, 20, 30, 32, 39], indicating that in at least some of these phenomena the noise sources could be non-Gaussian. The use of non-Gaussian noises in such studies is rare, mainly due to the difficulties of handling them and to the possibility of obtaining some analytical results when working with Gaussian (particularly white) noises.