ABSTRACT
Dynamical systems play a central role in applications of mathematics to natural and engineering sciences. However, dynamical systems governing real processes always contain some elements characterized by uncertainty or stochasticity. Uncertainties may arise in the system parameters, the boundary and initial conditions, and also in the ‘external forcing’ processes. Also, many problems are treated through the stochastic framework due to the incomplete or partial understanding of the governing physical laws. In all of the above cases the existence of random perturbations, combined with the complex dynamical mechanisms of the system itself can often lead to a rapid growth of the uncertainty in the dynamics and state of the system. Such rapid growth can distribute the uncertainties to a broadband spectrum of scales both in space and time, making the system state particularly complex.
