Bistable dynamics

Bistable dynamics describes a system that can settle into either of two distinct stable states for the same range of control parameters, with the actual state depending on the system's history — a property known as \u200bhysteresis. Unlike systems with a single equilibrium, bistable systems possess two attractors separated by an unstable threshold or separatrix; a perturbation large enough to push the system across this threshold triggers a rapid transition to the alternative state.

In the climate system, bistable dynamics appear in the \u200bAtlantic Thermohaline Circulation, which can operate in either a strong or weak mode depending on the history of freshwater forcing. The concept generalizes to ecology (lake eutrophication), genetics (toggle switches), and neuroscience (neural firing patterns). The mathematical framework is \u200bcatastrophe theory, which classifies how smooth changes in parameters can produce discontinuous state changes. See Critical transition and Attractor.