ANALYSIS OF RANDOM DYNAMICAL SYSTEMS BY INTERPOLATED CELL MAPPING

Abstract

A method of interpolated cell mapping (ICM) is developed for global analysis of random dynamical systems. In this method, one first analyzes a random system by constructing a uniform number of sample interpolated trajectories for each cell. More sample interpolated trajectories are then constructed for critical cell sensitive to random effects to characterize the global behaviour of the system. When applied to the global analysis of non-linear systems with uncertain external loadings or system parameters, the proposed method yields more precise results than the generalized cell mapping (GCM) method. These results agree well with those obtained by Monte Carlo simulation. Additionally, the proposed method allows global analyses of random systems to be improved easily when the original regions of study are too large to give precise analyses.