Abstract
Graphs are commonly used to represent natural and man-made dynamic systems such as food webs, economic and social networks, gene regulation, and the internet. We describe a conceptual framework to enable early warning of relevant phenomena that is based on an artificial time-based, evolving network graph that can give rise to one or more recognizable structures. We propose to quantify the dynamics using the method of delays through Takens’ Theorem to produce another graph we call the Phase Graph. The Phase Graph enables us to quantify changes of the system that form a topology in phase space. Our proposed method is unique because it is based on dynamic system analysis that incorporates Takens’ Theorem, Graph Theory, and Franzosi-Pettini (F-P) theorem about topology and phase transitions. The F-P Theorem states that the necessary condition for phase transition is a change in the topology. By detecting a change in the topology that we represent as a set of M-order Phase Graphs, we conclude a corresponding change in the phase of the system. The onset of this phase change enables early warning of emerging relevant phenomena.