SLIDE 15 Tipping point defined
❖ Let Wt(x0) denote the value of a deterministic
process at time t=0,1,…, where x0 is an input at t=0
❖ Let δ denote a small positive constant ❖ The process Wt(x0) has an (initial) tipping point at
x0=a when the values of Wt(a–δ) and Wt(a+δ) are very different for t≥T, where T is a positive constant
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If gradually adjusting the initial state causes a discontinuous jump in the state of a system at some future time, then the system has an initial tipping
- point. More generally, a tipping point (or critical point) is a narrow transition
domain separating two well-defined phases.
Explanation
❖ What the definition means is that small changes in
x0 near the threshold point cause the future values
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0% 25% 50% 75% 100% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30% 32% 34%
Resulting fraction of distrust Initial fraction of mistrust Distrust
Trust model has tipping point
❖ The input to the model is the
initial fraction of mistrust
❖ As this fraction goes from 14%
to 28%, the expected fraction of distrust increases from nearly
0% to nearly 100%
❖ There is a tipping point at 21%
initial mistrust
❖
W(21%–7% mistrust) ≈ 0% distrust
❖
W(21%+7% mistrust) ≈ 100% distrust
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Small changes to the initial percentage of mistrust around 21% leads to large changes in the expected value of the final percentage of distrust.