Qnoise : A Generator of Non-Gaussian Colored Noise

We introduce a software generator for a class of colored (self-correlated) and non-Gaussian noise, whose statistics and spectrum depend on two param- eters, q and τ. Inspired by Tsallis’ nonextensive formulation of statistical physics, the so-called q-distribution is a handy source of self-correlated noise for a large range of applications. The q-noise—which tends smoothly for q = 1 to Ornstein–Uhlenbeck noise with autocorrelation τ—is generated via a stochastic differential equation, using the Heun method (a second order Runge–Kutta type integration scheme). The algorithm is implemented as a stand-alone library in C++, and is made available as open source in the Github repository. Noise’ statistics can be specified handily; by only varying parameter q: it has compact support for q < 1 (sub-Gaussian regime) and finite variance up to q = 5/3 (supra-Gaussian regime). Once q is fixed, noise’ autocorrelation can be tuned independently by means of parameter τ. The presented qNoise generator provides a readily tool to modeling wide range of real-world noise types, and is suitable to study the effects of correlation and deviations from the normal distribution in systems of stochastic differen- tial equations, key to understand system dynamics in numerous applications. The effect of noises’ statistics on the response of a range of nonlinear systems is briefly discussed. In many of these examples, the systems’ response turns optimal for some q ̸= 1. Hence, this paper aims to introduce qNoise gen- erator for C++ at the class level and evaluate the kind of noise it generates, alongside their use in a range of applications