The concept of tipping points is powerful, but sometimes a bit muddled. Things that get described as tipping points often sound to me like mere dramatic events or nonlinear effects, simple thermodynamic irreversibilities, or exponential signals emerging unexpectedly from noise. These may play a role in tipping points, and lead to surprises, but I don’t think they capture the essence of the idea. You can see examples (good and bad) if you sift through the images describing tipping points on google.
I think of tipping points as a feedback phenomenon: positive feedback that amplifies a disturbance, such that change takes off, even if the disturbance is removed. The key outcome is a system that is stable or resistant to disturbances up to a point, beyond which surprising things may happen.
A simple example is sitting in a chair. The system has two stable equilibria: sitting upright, and lying flat on your back (tipped over). There’s also an unstable equilibrium – the precarious moment when you’re balanced on the back legs of the chair, and the force of gravity is neutral. As long as you lean just a little bit, gravity is a restoring force – it will pull you back to the desirable upright equilibrium if you pick up your feet. Lean a bit further, past the unstable tipping point, and gravity begins to pull you over backwards. Gravity gains leverage the further you lean – a positive feedback. Waving your arms and legs won’t help much; you’re going to be flat on your back.
A more generalized explanation is given in catastrophe theory. The interesting twist is that a seemingly-stable system may acquire tipping points unexpectedly as its parameters drift into regimes that create new stable and unstable points, leading to surprises. Even without structural change to the system, its behavior mode can change unexpectedly as the state of the system moves from locally-stable territory to locally-unstable territory, which occurs due to shifting loop dominance from nonlinearities. (Think of the financial crisis and some kinds of aircraft accidents, for example.)
Anyone know some nice, simple tipping point models? I think I’ll have to mine my archives for some concrete examples…