THE CELL-TO-CELL MAPPING TECHNIQUE AND CHAPMAN-KOLMOGOROV REPRESENTATION OF SYSTEM DYNAMICS

The cell to cell mapping technique (CCMT) is a numerical technique for the global analysis of non-linear dynamic systems. The CCMT is partic ularly useful if the system has a strange attractor. Using a Chapman-K olmogorov representation of system dynamics, two new CCMT algorithms a re presented which substantially reduce the computational time and com puter storage requirements compared to the conventional implementation of CCMT in the determination of the attractors of the system and thei r domains of attraction. The new algorithms are also advantageous when it is difficult to identify a unique probability density function (pd f) to represent the uncertainty in the system parameters and several p dfs need to be considered to assess the impact of the choice of the pd f on the predicted asymptotic system behavior. These features of the n ew algorithms are illustrated using a second order Duffing oscillator under harmonic forcing.