In mathematics, stability theory deals with the stability of the solutions of differential equations and dynamical systems. Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... Graph of a differential equation In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ... A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. ...

Definitions of stability include: Lyapunov stability, structural stability In mathematics, the notion of Lyapunov stability occurs in the study of dynamical systems. ... Structural stability is a mathematical concept concerning whether a given function is sensitive to a small perturbation. ...

For example, a differential equation may have a series of solutions that are attracted to a single, stable periodic orbit; such a series of solutions is known as a limit cycle. In mathematics, in the area of dynamical systems, a limit-cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches minus-infinity. ...