Noise injection on networked systems and correlation reduction for early warning signals

A tipping point is a significant change in the stability of a system caused by the gradual change of one parameter. Examples of tipping points are species extinction, species burst, and disease onset. We study tipping points as bifurcations in the deterministic part of a stochastic differential equation (SDE). We use this framework because we are able to account for how the external noise is exacerbated when a system is close to bifurcate. This phenomenon is called critical slowing down; it allows the use of variances of the components of a system as an indicator that a bifurcation is close. We call these variances early warning signals (EWSs).  

We study EWSs using SDEs on networked systems. The novelty of our approach is injecting noise to the nodes of a system to obtain good EWSs. We develop a method for noise injection that 1) reduces the correlation of the components of the system, and 2) leads to EWSs that spike later than EWSs of the same kind with no noise injection. The design of the noise injection that we create builds on an approximation of the original system by an Ornstein-Uhlenbeck process and its corresponding Lyapunov equation. This is a work in collaboration with Professor Naoki Masuda.