Instability

In dynamical systems instability means that some of the outputs or internal states increase with time, without bounds. Not all systems that are not stable are unstable; systems can also be marginally stable or exhibit limit cycle behavior. In structural engineering, a structural beam or column can become unstable when excessive compressive 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. Atmospheric instability is a major component of all weather systems on Earth. Stabilizability In the theory of dynamical systems, a state variable in a system is said to be unstable if it evolves without bounds. A system itself is said to be unstable if at least one of its state variables is unstable. In continuous time control theory, a system is unstable if any of the roots of its characteristic equation has real part greater than zero (or if zero is a repeated root). This is equivalent to any of the eigenvalues of the state matrix having either real part greater than zero, or, for the eigenvalues on the imaginary axis, the algebraic multiplicity being larger than the geometric multiplicity. The equivalent condition in discrete time is that at least one of the eigenvalues is greater than 1 in absolute value, or that two or more eigenvalues are equal and of unit absolute value. Buckling Elastic instability Drucker stability of a nonlinear constitutive model Biot instability (surface wrinkling in elastomers) Baroclinic instability 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.