Predicting critical transitions in complex systems

Abstract

In this study, we investigate the precursor phenomena seen as getting close to a bifurcation point which triggers a critical transition from one to another attractor state to discover novel early-warning signals for practical applications. An attractor is defined as a stable state to which all initial system states eventually converge. For each attractor in a multiple-attractor system, the perturbed states within a certain range around an attractor ultimately converge to the attractor. Such a region of convergence around the attractor is called the basin of attraction. First, the concept of critical slowing down is applied to seizure prediction in epilepsy patients. Critical slowing down means slower recovery from perturbations for an attractor, approaching a bifurcation point. Second, the concept of flickering is applied to investigate a precritical phenomenon during colorectal tumorigenesis. Under a noisy environment, the frequent flickering state transition occurs before a critical transition to an alternative state

from the impact of noise, the state of a system frequently switches back and forth between the basins of attraction for alternative attractors, and it increases the variation in the estimate of the respective basin sizes.