Complex network analysis of the exoplanetary observables

The more precise observations and dedicated missions in exoplanetary research provide a large amount of data that needs to be analyzed in a proper way. This analysis can happen from various point of view. In this work the powerful tools of nonlinear time series analysis and machine learning are used to describe and forecast the multi-planetary dynamics. Making use of the fact that the chaotic nature of a dynamical system can be analyzed quantitatively even if we have limited knowledge about the mathematical model behind it, we reproduce the dynamical characteristics of the planetary motion based only on different kind of observational data (radial velocity, transit times, astrometry). We propose a method using the complex network description of the phase space recurrences combined with supervised machine learning techniques (such as artificial neural networks) in order to discover and classify the stability of multi-planetary systems. The advantage of this method is that one can determine the quantitative ergodic measures of the dynamical system under study only from a scalar time series. Moreover, the state vector, reconstructed from the original signal, can be interpreted as a complex network and the corresponding random graph. Thus exoplanetary dynamics can be investigated from a network-based perspective and the well-known measures (like average path length, assortativity, clustering, or degree distribution) can be assigned to the underlying dynamics. This allows us to ignore the time consuming Bayesian analysis and Monte-Carlo simulations to obtain the initial conditions of N-body integrations.

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