title: Identifying early-warning signals of critical transitions with strong noise by dynamical network markers.
abstract: Identifying early-warning signals of a critical transition for a complex system is difficult, especially when the target system is constantly perturbed by big noise, which makes the traditional methods fail due to the strong fluctuations of the observed data. In this work, we show that the critical transition is not traditional state-transition but probability distribution-transition when the noise is not sufficiently small, which, however, is a ubiquitous case in real systems. We present a model-free computational method to detect the warning signals before such transitions. The key idea behind is a strategy: "making big noise smaller" by a distribution-embedding scheme, which transforms the data from the observed state-variables with big noise to their distribution-variables with small noise, and thus makes the traditional criteria effective because of the significantly reduced fluctuations. Specifically, increasing the dimension of the observed data by moment expansion that changes the system from state-dynamics to probability distribution-dynamics, we derive new data in a higher-dimensional space but with much smaller noise. Then, we develop a criterion based on the dynamical network marker (DNM) to signal the impending critical transition using the transformed higher-dimensional data. We also demonstrate the effectiveness of our method in biological, ecological and financial systems.
authors.affiliation: School of Mathematics, South China University of Technology, Guangzhou 510640, China.
authors.forename: Rui
authors.initials: R
authors.lastname: Liu
authors.affiliation: School of Computer Science and Engineering, South China University of Technology, Guangzhou 510640, China.
authors.forename: Pei
authors.initials: P
authors.lastname: Chen
authors.affiliation: Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan.
authors.forename: Kazuyuki
authors.initials: K
authors.lastname: Aihara
authors.affiliation: Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan.|Key Laboratory of Systems Biology, Innovation Center for Cell Signaling Network, Institute of Biochemistry and Cell Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, Shanghai 200031, China.
authors.forename: Luonan
authors.initials: L
authors.lastname: Chen