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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 ...
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 ).
Routh–Hurwitz stability criterion; Vakhitov–Kolokolov stability criterion; Barkhausen stability criterion; Stability may also be determined by means of root locus analysis. Although the concept of stability is general, there are several narrower definitions through which it may be assessed: BIBO stability; Linear stability; Lyapunov stability
The community context considers a relatively constant environment in which multiple stable states are accessible to populations or communities. This definition is an extension of stability analysis of populations (e.g., Lewontin 1969; Sutherland 1973) and communities (e.g., Drake 1991; Law and Morton 1993).
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]
An additional condition called "properness" or "radial unboundedness" is required in order to conclude global stability. Global asymptotic stability (GAS) follows similarly. It is easier to visualize this method of analysis by thinking of a physical system (e.g. vibrating spring and mass) and considering the energy of such a system. If the ...
LaSalle's invariance principle (also known as the invariance principle, [1] Barbashin-Krasovskii-LaSalle principle, [2] or Krasovskii-LaSalle principle) is a criterion for the asymptotic stability of an autonomous (possibly nonlinear) dynamical system.
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...