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In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation , for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature ...
This analogy with mechanical equilibrium motivates the terminology of stability and instability. In mathematics , and especially algebraic geometry , stability is a notion which characterises when a geometric object , for example a point , an algebraic variety , a vector bundle , or a sheaf , has some desirable properties for the purpose of ...
Numerical stability, a property of numerical algorithms which describes how errors in the input data propagate through the algorithm; Stability radius, a property of continuous polynomial functions; Stable theory, concerned with the notion of stability in model theory; Stability, a property of points in geometric invariant theory
Stability generally increases to the left of the diagram. [1] Some sink, source or node are equilibrium points . 2-dimensional case refers to Phase plane . In mathematics , an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable .
The state is neutral to the lowest order and nearly remains in equilibrium if displaced a small amount. To investigate the precise stability of the system, higher order derivatives can be examined. The state is unstable if the lowest nonzero derivative is of odd order or has a negative value, stable if the lowest nonzero derivative is both of ...
Elasticity (physics) – Physical property when materials or objects return to original shape after deformation; Elastic modulus – Physical property that measures stiffness of material; Elastography – Set of imaging methods for determining soft-tissue hardness; Hardness – Measure of a material's resistance to localized plastic deformation
A graph of the potential energy of a bistable system; it has two local minima and .A surface shaped like this with two "low points" can act as a bistable system; a ball resting on the surface can only be stable at those two positions, such as balls marked "1" and "2".
In the control system theory, the Routh–Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time-invariant (LTI) dynamical system or control system. A stable system is one whose output signal is bounded; the position, velocity or energy do not increase to infinity as ...