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This paper addresses the need of characterizing system instability toward critical transitions in complex systems. We propose a novel information dynamic spectrum framework and a probabilistic light cone method to automate the analysis. Our framework uniquely investigates heterogeneously networked dynamical systems with transient directional influences, which subsumes unidirectional diffusion dynamics. When the observed instability of a system deviates from the prediction, the method automatically indicates the approach of an upcoming critical transition. We provide several demonstrations in engineering, economics, and social systems. The results suggest that early detecting critical transitions of synchronizations, sudden collapse, and exponential growth is possible.

Information dynamic spectrum characterizes system instability toward critical transitions