a Space Research Centre, Polish Academy of Sciences, Bartycka 18 A, 00-716 Warsaw, Poland b Faculty of Mathematics and Natural Sciences, College of Sciences, Cardinal Stefan Wyszyński University, Dewajtis 5, 01-815 Warsaw, Poland
Abstract:
We consider periodic and chaotic dynamics of discrete nonlinear maps in the presence of dynamical noise. We show that dynamical noise corrupting dynamics of a nonlinear map may be considered as a measurement “pseudonoise” with the distribution determined by the Jacobian of the map. The formula for the distribution of the measurement “pseudonoise” for one-dimensional quadratic maps has also been obtained in an explicit form. We expect that our results apply to an arbitrary distribution of low-level dynamical noise and hope that these results could help to find a universal method of discriminating dynamical from measurement noise.