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The concept of ecological stability emerged in the first half of the 20th century. With the advancement of theoretical ecology in the 1970s, the usage of the term has expanded to a wide variety of scenarios. This overuse of the term has led to controversy over its definition and implementation. [3]
Directional stability, the tendency for a body moving with respect to a medium to point in the direction of motion; Elastic stability, the resistance of a structural member to buckling; Flight dynamics, including longitudinal stability; Nyquist stability criterion, defining the limits of stability for pole-zero analysis in control systems
A method is L-stable if it is A-stable and () as , where is the stability function of the method (the stability function of a Runge–Kutta method is a rational function and thus the limit as + is the same as the limit as ).
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 ...
The longitudinal stability of an aircraft, also called pitch stability, [2] refers to the aircraft's stability in its plane of symmetry [2] about the lateral axis (the axis along the wingspan). [1] It is an important aspect of the handling qualities of the aircraft, and one of the main factors determining the ease with which the pilot is able ...
Slope stability analysis is a static or dynamic, analytical or empirical method to evaluate the stability of slopes of soil- and rock-fill dams, embankments, excavated slopes, and natural slopes in soil and rock.
The concept of allostasis, maintaining stability through change, is a fundamental process through which organisms actively adjust to both predictable and unpredictable events... Allostatic load refers to the cumulative cost to the body of allostasis, with allostatic overload... being a state in which serious pathophysiology can occur...
Structural stability of the system provides a justification for applying the qualitative theory of dynamical systems to analysis of concrete physical systems. The idea of such qualitative analysis goes back to the work of Henri Poincaré on the three-body problem in celestial mechanics .