Definitions for different types of tipping points are presented in the papers by Lamberson and Page (2012) and by Lenton (2013).
According to Lamberson and Page (2012), there are different types of tips.
- First, if gradual change in the tipping variable xt results in eventual discontinuities in the tipping variable itself, without intervention of another system variable, the tip is termed Direct. Direct tips can be unstable equilibria (metastable), basin borders (plateaus), or chaotic points that are sensitive to initial conditions.
- In the more general case, where changes in the threshold variable yt are responsible for the eventual changes in the tipping variable, the tip is termed Contextual. Contextual tips can be bifurcations or phase transitions.
Bifurcations and phase transitions are also described in detail by Lenton (2013). Figure 2 in the Lenton (2013) paper depicts the topology of these tips.