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 particularly useful if the system has a strange attractor. Using a Chapman-Kolmogorov representation of system dynamics, two new CCMT algorithms are presented which substantially reduce the computational time and computer storage requirements compared to the conventional implementation of CCMT in the determination of the attractors of the system and their domains of attraction. The new algorithms are also advantageous when it is difficult to identify a unique probability density function (pdf) to represent the uncertainty in the system parameters and several pdfs need to be considered to assess the impact of the choice of the pdf on the predicted asymptotic system behaviour. These features of the new algorithms are illustrated using a second order Duffing oscillator under harmonic forcing.