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The term dynamical instability (or dynamic instability, or just instability) is a condition of dynamical system such that a perturbation encourages its own growth, i.e., a positive feedback situation.
The term dynamical indicates something with movement, often even before the instability occurs: for example, the conditions that produce some periodic motion growing to the point that its negative feedback becomes positive. But I believe the term is also used for conditions that began their movement as they become unstable. In astronomy, the term dynamical instability is common in a number of areas, and undoubtedly could be applied in many more:
An example of instability that termed other than dynamical might be a chemical mixture that is out of equilibrium.