Generalized cell mapping for randomly perturbed dynamical systems (Q2765238)

The cell mapping approach is used to analyze dynamical systems under random perturbations. The generalized cell mapping method is analysed from the measure theoretic viewpoint. The study of the graph structure is carried out using the algorithm of Tarjan, that allows to compute the number of steps it takes minimally to move from one cell to its attractor on the way. For higher efficiency of the method, an adaptive algorithm has been developed. The cells need not be chosen uniformly but can be of any size and shape if non-overlapping and covering the cell space completely. The adaptive algorithm is started with few cells. The invariant measure is approximated and those cells where the invariant measure changes most are subdivided. Basin boundaries are refined using a geometric criterion. The transition probabilities are computed by the exhaustion method which yields an error estimate.