Instability

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 characteristic equation 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 can take the form of buckling or crippling. The general field of study is called structural stability.

Fluid instabilities
Fluid instabilities occur in liquids, gases and plasmas, and are often characterized 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
 * Atmospheric instability
 * Hydrodynamic instability or dynamic instability (atmospheric dynamics)
 * Inertial instability; baroclinic instability; symmetric instability, conditional symmetric or convective symmetric instability; barotropic instability; Helmholtz or shearing instability; rotational instability
 * Hydrostatic instability or static instability/vertical instability (parcel instability), thermodynamic instability (atmospheric thermodynamics)
 * Conditional or static instability, buoyant instability, latent instability, nonlocal static instability, conditional-symmetric instability; convective, potential, or thermal instability, convective instability of the first and second kind; absolute or mechanical instability
 * Bénard instability
 * Drift mirror instability
 * Kelvin–Helmholtz instability (similar, but different from the diocotron instability in plasmas)
 * Rayleigh–Taylor instability
 * Plateau-Rayleigh instability (similar to the Rayleigh–Taylor instability)
 * Richtmyer-Meshkov instability (similar to the Rayleigh–Taylor instability)

Plasma instabilities
Plasma instabilities can be divided into two general groups (1) hydrodynamic instabilities (2) kinetic instabilities. Plasma instabilities are also categorised into different modes:

Source: Andre Gsponer, "Physics of high-intensity high-energy particle beam propagation in open air and outer-space plasmas" (2004)