Where does tipping point collide?

Morton Grodzins's 1957 Metropolitan Segregation named the tip point: the share of arriving minority residents at which the remaining white residents begin to leave in numbers, so a mixed neighborhood flips rapidly toward full resegregation. Thomas Schelling's 1971 Dynamic models of segregation showed formally how mild individual preferences about who lives nearby can produce this sharp collective switch. Here the referent is a demographic threshold in where people choose to live, counted as a percentage of a local population, and it is unrelated to a subsystem of the planet's climate or a type of transition in a set of equations.[1][2]

Unit

One neighborhood's minority share, as a percentage of local residents

Recovery means

Not applicable

Measured by

Estimated from census tract composition and the rate of resident turnover as minority share rises

Ashwin, Wieczorek, Vitolo, and Cox's 2012 Tipping points in open systems gave the term a formal reading in the theory of dynamical systems, classifying three ways a system can tip: a slow change in a parameter that destroys a stable state (bifurcation-induced), a chance push by random fluctuation across a boundary (noise-induced), and a change too fast for the system to track even with no bifurcation present (rate-induced). Here the referent is a property of the equations themselves, defined by the mathematical structure of the transition, not a specific neighborhood or a specific piece of the climate, although the same mathematics is used to model both.[3]

Unit

One classified transition in a dynamical system, by its triggering mechanism

Recovery means

Depends on the mechanism; a rate-induced tip can reverse if the driver slows, while a bifurcation-induced one usually cannot

Measured by

Identified analytically from a model's bifurcation structure and, empirically, through early-warning signals such as critical slowing down