A universal indicator of critical state transitions in noisy complex networked systems

Junhao Liang,Yanqing Hu,Tianshou Zhou,Guanrong Chen

doi:10.1038/srep42857

Abstract

Critical transition, a phenomenon that a system shifts suddenly from one state to another, occurs in many real-world complex networks. We propose an analytical framework for exactly predicting the critical transition in a complex networked system subjected to noise effects. Our prediction is based on the characteristic return time of a simple one-dimensional system derived from the original higher-dimensional system. This characteristic time, which can be easily calculated using network data, allows us to systematically separate the respective roles of dynamics, noise and topology of the underlying networked system. We find that the noise can either prevent or enhance critical transitions, playing a key role in compensating the network structural defect which suffers from either internal failures or environmental changes, or both. Our analysis of realistic or artificial examples reveals that the characteristic return time is an effective indicator for forecasting the sudden deterioration of complex networks.

Highlights

Critical transition, a phenomenon that a system shifts suddenly from one state to another, occurs in many real-world complex networks
Our consideration is based on two reasons: (1) stochastic fluctuations exist extensively in many real-world complex networks, e.g., biochemical reaction networks are inherently noisy due to low copy numbers of reactive species[29,30,31]; (2) homogeneous networks tend to evolve through critical transitions in response to external or environmental changes, whereas heterogeneous networks tend to change gradually, implying that no critical transition happens[25,32,33,34]
We analyze the effect of random attacks on critical transitions in a complex network, testing whether there is a steady state with a small magnitude if the original system is at a steady state with a large magnitude

Summary

Introduction

A phenomenon that a system shifts suddenly from one state to another, occurs in many real-world complex networks. When a stochastic system is close to its tipping point, a phenomenon called “flickering”[24,25] may occur, that is, the system may switch between several potential states due to the effect of stochastic fluctuations, leading to multimodality or even vibration This is another kind of early-warning signal that in general cannot be predicted by the occurrence of critical slowing down. By the effective stability approximation[38], we derive an analytical expression for the noise-dependent characteristic return time defined as the negative inverse of the mean characteristic value of the 1-D indicative system This characteristic time can well capture early-warning signals of the original large-scale system since it tends to infinity when the system approaches to a tipping point, and it can be taken as an effective indicator of critical transitions. This indicator allows us to systematically separate the respective roles of the dynamics, noise and topology of a complex network in controlling its sudden deterioration

Methods

Results

Conclusion