Instability

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Instability in systems is generally characterized by some of the outputs or internal states growing without bounds. Not all systems that are not stable are unstable; systems can also be marginally stable or exhibit limit cycle behavior.

In control theory, a system is unstable if any of the roots of its S-function has real part greater than zero. This is equivalent to any of the eigenvalues of the state matrix having real part greater than zero.

In structural engineering, a structure can become unstable when excessive load is applied. Beyond a certain threshold, structural deflections magnify stresses, which in turn increases deflections. This is can take the form of buckling or crippling. The general field of study is called structural stability.

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Fluid instabilities

Fluid instabilities occur in liquids, gases and plasmas, and are often characterised by the shape that form; they are studied in fluid dynamics and magnetohydrodynamics. Fluid instabilities include:

Ballooning mode instability (some analogy to the Rayleigh-Taylor instability); found in the magnetosphere
Baroclinic Instability
Benard Instability
Drift mirror instability
Kelvin-Helmholtz instability (similar, but different to the diocotron instability in plasmas)
Rayleigh-Taylor instability

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Plasma instabilities

Plasma instabilities can be divided into two general groups (1) hydrodynamic instabilities (2) kinetic instabilities.

Bennett pinch instability (also called the z-pinch instability )
Beam acoustic instability
Bump-in-tail instability
Buneman instability (same as Farley-Buneman instability?)
Cherenkov instability
Chute instability
Coalescence instability
Collapse instability
Counter-streaming instability
Cyclotron instabilities, including:

Alfven cyclotron instability
Electron cyclotron instability
Electrostatic ion cyclotron Instability
Ion cyclotron instability
Magnetoacoustic cyclotron instability
Proton cyclotron instability
Nonresonant Beam-Type cyclotron instability
Relativistic ion cyclotron instability
Whistler cyclotron instability

Diocotron instability (similar to, but different to the Kelvin-Helmholtz instability).
Disruptive instability (in tokamaks)
Double emission instability
Drift wave instability
Edge-localised modes [1]
Farley-Buneman instability
Fan instability
Filamentation instability
Firehose instability (also called Hose instability)
Flute instability
Free electron maser instability
Gyrotron instability
Helical instability (helix instability)
Helical kink instability
Hose instability (also called Firehose instability)
Interchange instability
Ion beam instability
Kink instability
Lower hybrid (drift) instability (in the Critical ionization velocity mechanism)
Magnetic drift instability
Modulation instability
Non-Abelian instability
Non-linear coalescence instability
Oscillating two stream instability, see two stream instability
Pair instability
Parker instability
Peratt instability (stacked toroids)
Pinch instability
Sausage instability
Slow Drift Instability
Tearing mode instability
Two stream instability
Weak beam instability
Weibel instability
z-pinch instability, also called Bennett pinch instability