This paper introduces two definitions for the concept of "tipping point" and investigates these with respect to each other and their relationship to real-world and experimental data. We introduce mathematical definitions which are called "hard" and "natural" tipping points, the first more objective while the second occurs more frequently in actual instances. Theorems which relate these to each other are given in this paper. Using the notion of natural tipping point, we investigate two instances. In the first, we look at a model of battery endurance and show that a natural tipping point occurs relative to that function. Next, we introduce a powerful model function we call the "TC Tipping Point Model Function". We show that this has both hard and natural tipping points. We also show how it can be used to model simulation data using a simple word game we have programmed and with an application of the Levenberg-Marquardt method.
['Catherine Cavagnaro', 'John Tiller']
Tipping Points and Models