On the effects of random time in dynamical systems. (Q2776855)

The author analyzes the effects of internal random time in some dynamical systems. He assumes that this relative time is equal to the absolute time disturbed by an additive random term in the form of a Gaussian white noise, and it is shown that, as a result of the special properties of Brownian motion, it is recommended to use Taylor expansions up to the second order, in the approximations (whilst the first order is usually sufficient for deterministic systems). He examines the consequences of this property on the dynamical system. This analysis is more especially relevant to biological systems, and to dynamical systems involving human factors. It is well-known, for instance, that the scale of time is not the same for senior citizens and teenagers.