Bistability

The two states 1 and 3 are stable, the transition state 2 is unstable.

Bistability (from Latin bi = two and Latin stabilis = steadfast, stable ) is the property of some systems to be able to assume two possible stable states, but only to change from one to the other by an external impulse. These systems are then called bistable systems. It is important that these states can be assumed with one and the same parameter values , in contrast to, for example , ultra-sensitivity , where a sharp transition is caused by changing parameter values. Usually, the states are stationary states in the sense of dynamic equilibria .

Mathematical description

Bistable behavior is usually brought about by positive feedback . Each of the states thereby stabilizes itself.

If the behavior of a system can be described by differential equations , then bistability can already occur in one-dimensional systems, i.e. That is, an independent variable is sufficient , while two-dimensional systems are necessary for oscillations . The differential equations must, however, be non-linear. In linear systems only three cases are possible: There is exactly one steady state, no steady state at all or a continuum of such states. In the case of bistability, however, two isolated states must occur.

The fork bifurcation shows the transition from a stable to a bistable system from left to right. Thick black curves: stable states; dashed red: unstable (unstable) state.

The transition between a stable and a bistable system can be shown with the help of the fork bifurcation diagrams shown on the right .

Examples from various fields

An example from everyday life is a light switch with snap contact : as long as it is not touched, it remains in one position ( on or off ). After releasing it, it either jumps back to the old position (not pressed firmly enough) or to the new position (pressed firmly enough for normal operation).

Further examples from the field of technology are the flip-flop in electronics or bistable springs in mechanics . Even complex systems, such as democratic states with two large parties that alternately win a majority in parliament, can at least temporarily be bistable.

Web links

Wiktionary: bistable  - explanations of meanings, word origins, synonyms, translations

credentials

• W. Ebeling, R. Feistel, Physics of Self-Organization and Evolution. Akademie-Verlag, Berlin 1982