On Stochastic Analysis Approaches for Comparing Complex Systems

We compare two probabilistic approaches that have been proposed for the study and comparison of data obtained from experiment or simulations of a dynamical systems model. Both the approaches aim to carry out spectral analysis using a time-series data that is generated by a dynamical system. The first approach is based on constructing the so-called harmonic averages from the time-series data [1] and the second is an approach based on construction of a Markov chain from the data [2]. Results of the comparison using time-series data from a combustion model is provided.