Bistable

Bistable refers to a system that possesses two distinct stable equilibrium states under a given set of parameters. Each state is locally stable, meaning that small disturbances cause the system to return to that state. Between the two stable equilibria lies an unstable equilibrium that serves as a boundary between their basins of attraction. As a result, the system can reside in either state for extended periods, and transitions between states typically require a sufficiently large external input or perturbation. The term is common in physics, engineering, chemistry, and biology.

In dynamical systems terms, bistability arises from nonlinearity and feedback that create a double-well potential or an S-shaped response. The two stable fixed points have Jacobian eigenvalues with negative real parts, while the unstable fixed point has a positive eigenvalue along at least one direction. In many systems, switching exhibits hysteresis: increasing an input moves the system from one state to the other at a threshold, while decreasing it returns to the original state at a different threshold.

Examples span multiple disciplines. Mechanical systems such as a buckled beam or a snap-through arch display two stable configurations. Electrical circuits use bistable elements like flip-flops and latches to store a bit of information. Optical systems can show optical bistability in nonlinear cavities, with low- and high-transmission states. In chemistry and biology, the genetic toggle switch in synthetic biology demonstrates bistability, and autocatalytic chemical reactions can sustain two alternative kinetic states.

Applications of bistability include memory storage, switches, and sensors. The concept also highlights challenges in noisy environments where random fluctuations can trigger unintended transitions. Analysis often employs phase-plane methods, energy landscapes, or bifurcation diagrams to identify stable states and transition thresholds.