Table 2.

Glossary for Critical State Transitions and Attractors in Systems Medicine.

Term	Definition	Example
Alternative stable states	Different steady states of the very same system can be realized under the same external conditions, depending on history	Healthy State (fasting glucose <115 mg/dL) vs. Diabetic State (fasting glucose >180 mg/dL) Since the pathological state is also a stable state (a new equilibrium) reversal is difficult, as best illustrated in the inherent challenge of weight loss by diet
Bifurcation (Critical State Transitions)	The current stable state of a system disappears due to (slow) change of system characteristics and the system is forced to move to an alternative stable state	During the process of gradual health deterioration (e.g., fasting glucose >115 mg/dL – prediabetic state), poor diet results in a sudden catastrophic shift to a disease state that self-stabilizes in the new equilibrium (Figure 2)
Attractor	An equilibrium state to which a system converges after some time; a stable steady state.	After an oral glucose tolerance test, blood glucose increases to an unstable value (>200 mg/dL) that will finally decrease to the health steady state value (<115 mg/dL)
Basin of attraction	The entire set of initial conditions from which the system automatically moves to an attractor	Temporary deviations from an equilibrium state following acute perturbations after which the systems resettle in the steady state manifest the basin of attraction – e.g., normoglycemia following a large meal that caused a peak in blood glucose
Potential U(x)	A mathematical quantity that captures the “driving force” in a dynamical system, and can be graphed as the elevation over each state space position × (a state variable) to obtain a landscape picture (potential well)	Can be approximated as the inverse of the t probability P(x) to find individual in a population at that state space position x, where × is a state variable, e.g., x = fasting glucose (mg/dL)
Threshold	A point where the system is very sensitive to changing conditions, e.g., at the “cusp” between two basins of attraction. In a critical transition, the threshold becomes a tipping point	In a prediabetic individual, when the basin of attraction for glucose homeostasis is flat and blood glucose reaches a borderline value, e.g., >115 mg/dL, the individual is more sensitive to glucose challenge.
Tipping point	The point in a critical transition at which the system flips to another attractor state	A specific value of a parameter × (characterizing disease progression) at which the system undergoes a critical state transition and moves to a new attractor.