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In a dynamical system, multistability is the property of having multiple stable equilibrium points in the vector space spanned by the states in the system. By mathematic necessity, there must also be unstable 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.


Main article: 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[edit]

Main article: Butterfly effect
Further information: Chaos theory
See also: Path dependence

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 chaos theory, this is called the butterfy effect. In economics and social sciences, path dependence is the term for divergent directions of development. Some path dependence processes are adequately described by multistability, by being initially sensitive to input, before possibly reaching a stagnant state, for example market share instability, that can develop into a stable monopoly for one of multiple possible vendors.

Multistable perception[edit]

Ambiguous images

In vision science, multistable perception characterizes the wavering percepts that can be brought about by certain visually ambiguous pattern such as the Necker cube, monocular rivalry or binocular rivalry. Through lateral inhibition, a pattern in which one image, when stimulated, inhibit the activity of neighboring images.

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