Chaos-induced hindrance of connectivity detection and topological unpredictability

The experimental assessment of networks within a complex system requires the inference of links. A common way to detect a link relies on the assumption that time series recorded out of two nodes contain sufficient shared information so as to detect a correlation, using either linear measures or more sensitive information-theoretical tools. While this assumption is theoretically granted for any system described by deterministically coupled differential equations, in an experimental scenario the emergence of chaotic regimes can hinder its validity. In this work we explore the issue of assessing connectivity in the prototypical case of a linear network of nonlinear oscillators, experimentally-implemented via a scalable electronic analog circuitry. Despite strong coupling, the assessed connectivity strength decays for an increasing length of the network. This phenomenon, which is interpreted in terms of a “topological unpredictability” of chaos, eventually leads to an apparent lack of connection between nodes that, in reality, are physically coupled. Our results provide insights on the difficulty of inferring links out of time series, with implications in the identification of networks in real systems, for example in Earth science and neuroscience. • In a complex system, identifying collective behaviors is a challenging issue. • Is correlation between networked systems in chaotic regimes detectable? • The issues is addressed in a linear network of Burridge–Knopoff oscillators. • Beyond a topological horizon, subsystems happen to be mutually uncorrelated. • Results are interpreted in terms of a “topological” unpredictability due to chaos.