On the robustness of the detection of relevant sets in complex dynamical systems

The identification of system’s parts that rule its dynamics and the understanding of its dynamical organisation is a paramount objective in the analysis of complex systems. In previous work we have proposed the Dynamical Cluster Index method, which is based on information-theoretical measures. This method makes it possible to identify the components of a complex system that are relevant for its dynamics as well as their relation in terms of information flow. Complex systems’ organisation is often characterised by intertwined components. The detection of such dynamical structures is a prerequisite for inferring the hierarchical organisation of the system. The method relies on a ranking based on a statistical index, which depends on a reference system (the homogeneous system) generated according to a parametrised sampling procedure. In this paper we address the issue of assessing the robustness of the method against the homogeneous system generation model. The results show that the method is robust and can be reliably applied to the analysis of data from complex system dynamics in general settings, without requiring particular hypotheses.