Part of mathematics that addresses the stability of solutions
For the branch of model theory, see stable theory.
Stability diagram classifying Poincaré maps of linear autonomous system as stable or unstable according to their features. Stability generally increases to the left of the diagram.[1] Some sink, source or node are equilibrium points.
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 at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.
In dynamical systems, an orbit is called Lyapunov stable if the forward orbit of any point is in a small enough neighborhood or it stays in a small (but perhaps, larger) neighborhood. Various criteria have been developed to prove stability or instability of an orbit. Under favorable circumstances, the question may be reduced to a well-studied problem involving eigenvalues of matrices. A more general method involves Lyapunov functions. In practice, any one of a number of different stability criteria are applied.
^Egwald Mathematics - Linear Algebra: Systems of Linear Differential Equations: Linear Stability Analysis Accessed 10 October 2019.
In mathematics, stabilitytheory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations...
Hegemonic stabilitytheory (HST) is a theory of international relations, rooted in research from the fields of political science, economics, and history...
important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple...
concepts of stabilitytheory to broader contexts, such as simple and NIP theories. A common goal in model theory is to study a first-order theory by analyzing...
contributed to the establishment of control stability criteria; and from 1922 onwards, the development of PID control theory by Nicolas Minorsky. Although a major...
the term "Theory of Models" in publication in 1954. Since the 1970s, the subject has been shaped decisively by Saharon Shelah's stabilitytheory. Compared...
cohesion Political decay Economic stability Hegemonic stabilitytheory Ake, Claude (1975). "A Definition of Political Stability". Comparative Politics. 7 (2):...
Look up stability in Wiktionary, the free dictionary. Stability may refer to: Stabilitytheory, the study of the stability of solutions to differential...
In control theory and stabilitytheory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German...
In control theory, and especially stabilitytheory, a stability criterion establishes when a system is stable. A number of stability criteria are in common...
numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context...
can be treated as a fluid and analyzed with the theory of magnetohydrodynamics (MHD). MHD stability is necessary for stable operation of magnetic confinement...
signal processing, specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for signals and systems that take inputs...
Dependency theory is the idea that resources flow from a "periphery" of poor and exploited states to a "core" of wealthy states, enriching the latter at...
In signal processing and control theory, the Jury stability criterion is a method of determining the stability of a linear discrete time system by analysis...
Henri Poincaré. Structural stability of non-singular smooth vector fields on the torus can be investigated using the theory developed by Poincaré and Arnaud...
exponentially stable over a certain range of inputs. Marginal stability Control theory State space (controls) David N. Cheban (2004), Global Attractors...
from where it started without limit. Marginal stability, like instability, is a feature that control theory seeks to avoid; we wish that, when perturbed...
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear...
transform, Z transform, Bode plot, root locus, and Nyquist stability criterion. Nonlinear control theory covers a wider class of systems that do not obey the...
propose power-based theories of regimes based on hegemonic stabilitytheory. Regime theory may appear to counter hegemonic stabilitytheory sometimes, but...
Set theory — Shape theory — Small cancellation theory — Spectral theory — Stabilitytheory — Stable theory — Sturm–Liouville theory — Surgery theory — Twistor...
Hegemonic StabilityTheory." International Organization 39 (4): pp. 580–614. Grunberg, Isabelle (1990). "Exploring the ‘Myth' of Hegemonic Stability." International...
development of the stabilitytheory of a dynamical system, as well as for his many contributions to mathematical physics and probability theory. Lyapunov was...
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