In a

dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a ...

, multistability is the property of having multiple stable equilibrium points in the

vector space In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', may be added together and multiplied ("scaled") by numbers called '' scalars''. Scalars are often real numbers, but can ...

spanned by the states in the system. By mathematical necessity, there must also be unstable equilibrium points between the stable points. Points that are stable in some dimensions and unstable in others are termed unstable, as is the case with the first three

Lagrangian points In celestial mechanics, the Lagrange points (; also Lagrangian points or libration points) are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Mathematically, this involves the solution of t ...

Bistability

Bistability is the special case with two stable equilibrium points. It is the simplest form of multistability, and can occur in systems with only one state variable, as it only takes a one-dimensional space to separate two points.

Initial instability

Near an unstable equilibrium, any system will be sensitive to noise, initial conditions and system parameters, which can cause it to develop in one of multiple divergent directions. In economics and social sciences, path dependence gives rise to divergent directions of development. Some path dependent processes are adequately described by multistability, by being initially sensitive to input, before reaching a stagnant state – for example

market share Market share is the percentage of the total revenue or sales in a market that a company's business makes up. For example, if there are 50,000 units sold per year in a given industry, a company whose sales were 5,000 of those units would have a ...

instability, which can develop into a stable

monopoly A monopoly (from Greek language, Greek el, μόνος, mónos, single, alone, label=none and el, πωλεῖν, pōleîn, to sell, label=none), as described by Irving Fisher, is a market with the "absence of competition", creating a situati ...

for one of multiple possible vendors.

Multistable perception

In vision science,

multistable perception Multistable perception (or bistable perception) is a perceptual phenomenon in which an observer experiences an unpredictable sequence of spontaneous subjective changes. While usually associated with visual perception (a form of optical illusion), ...

characterizes the wavering percepts that can be brought about by certain visually ambiguous pattern such as the

Necker cube The Necker cube is an optical illusion that was first published as a Rhomboid in 1832 by Swiss crystallographer Louis Albert Necker. It is a simple wire-frame, two dimensional drawing of a cube with no visual cues as to its orientation, so it ...

monocular rivalry Monocular rivalry is a phenomenon of human visual perception that occurs when two different images are optically superimposed. During prolonged viewing, one image becomes clearer than the other for a few moments, then the other image becomes clear ...

binocular rivalry Binocular rivalry is a phenomenon of visual perception in which perception alternates between different images presented to each eye. When one image is presented to one eye and a very different image is presented to the other (also known as dic ...

. Through lateral inhibition, a pattern in which one image, when stimulated, inhibit the activity of neighboring images.

External links

Definition of multistability from icbm.de
Optical illusions {{sci-stub