Uncertainty propagation in dynamical systems

Dynamical propagation of parametric and initial condition uncertainty is studied. The notion of input measure of an observable is defined and its propagation to output measure of the observable is studied by means of transfer operators. Uncertainty of these measures is defined in terms of their cumulative probability distributions. Comparison with alternative uncertainty metrics such as variance and entropy is pursued. The developed formalism is illustrated through an analysis of the effect of pitchfork bifurcation on uncertainty. Finally, the implications of these concepts in the design of nonlinear systems are discussed.