Fig. 2

The performance of sKLD based on a dataset of numerical simulation. a A network with eight nodes governed by a model is represented in Michaelis-Menten form, based on which the numerical simulation is conducted. b The curve of sKLD score defined in Eq. (2). It is obvious that the sKLD would abruptly increase when the system is near the critical point, i.e., s = 0, which is in accordance with the bifurcation parameter value at s = 0 (see Eq. (S3) in Additional file 1: A). c It is seen that the perturbed frequency Q presents two peaks when the system approaches the tipping point, i.e., s = 0, comparing with that in a normal state (s = − 0.2) or a disease state (s = 0.1) and there is no significant difference in three stages of disease progression for the reference P