The stability of a general dynamical system with no input can be described with Lyapunov stability criteria.

To address these questions several notions of stability have been introduced in the study of dynamical systems, such as Lyapunov stability or structural stability.

* Stability theory, the study of the stability of solutions to differential equations and dynamical systems

While he is best known for the Kolmogorov – Arnold – Moser theorem regarding the stability of integrable Hamiltonian systems, he made important contributions in several areas including dynamical systems theory, catastrophe theory, topology, algebraic geometry, classical mechanics and singularity theory, including posing the ADE classification problem, since his first main result — the partial solution of Hilbert's thirteenth problem in 1957 at the age of 19.

Lyapunov is known for his development of the stability theory of a dynamical system, as well as for his many contributions to mathematical physics and probability theory.

Phase space of a dynamical system with focal stability.

This notion has a strong connection with Lyapunov stability, where the storage functions may play, under certain conditions of controllability and observability of the dynamical system, the role of Lyapunov functions.

So he had to introduce another ad-hoc hypothesis: non-electric binding forces ( Poincaré stresses ) that ensure the Electron's stability, give a dynamical explanation for length contraction, and thus hide the motion of the stationary aether.

Various types of stability may be discussed for the solutions of differential equations describing dynamical systems.

Formally, knowing the step response of a dynamical system gives information on the stability of such a system, and on its ability to reach one stationary state when starting from another.

Early studies of the dynamical stability of, which used a small number of test particles spread over the uncertainties of just a few orbital parameters that were derived from a limited observation arc, suggested that is on a remarkably stable orbit, because most test particles remained on trojan orbits for 5 Gyr.

Secular resonances were found not to contribute to the dynamical stability of.

In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems.

: See Lyapunov stability, which gives a definition of asymptotic stability for more general dynamical systems.

Ecology borrows the idea of neighborhood stability and a domain of attraction from dynamical systems theory.

In mathematics, structural stability is a fundamental property of a dynamical system which means that the qualitative behavior of the trajectories is unaffected by C < sup > 1 </ sup >- small perturbations.

Structural stability of the system provides a justification for applying the qualitative theory of dynamical systems to analysis of concrete physical systems.

Fundamental works of Nikolay Bogoliubov were devoted to asymptotic methods of nonlinear mechanics, quantum field theory, statistical field theory, variational calculus, approximation methods in mathematical analysis, equations of mathematical physics, theory of stability, theory of dynamical systems, and to many other areas.

He was a founder of the theory of self-exciting oscillation and deeply developed the theory of stability of dynamical systems by introducing ( together with Lev Pontryagin ) the notion of structural stability.

When the frequency response characteristics of practical components are considered, their effect on stability does not present the most serious limit on the system loop gain.

Some argue that the openness of the country's political system has been a significant factor in Botswana's stability and economic growth.

The objective is to ensure the stability and efficiency of the system and compliance to rules and regulations ; the bank pursues it through secondary legislation, controls and cooperation with governmental authorities.

Nelson ordered the fleet to slow down at 16: 00 to allow his ships to rig " springs " on their anchor cables, a system of attaching the bow anchor that increased stability and allowed his ships to swing their broadsides to face an enemy while stationary.

The stability of a colloidal system is the capability of the system to remain as it is.

MKCL emphasises reliability, stability and overall code quality through a heavily reworked, natively multi-threaded, runtime system.

The usual objective of a control theory is to calculate solutions for the proper corrective action from the controller that result in system stability, that is, the system will hold the set point and not oscillate around it.

Independently, Adolf Hurwitz analyzed system stability using differential equations in 1877, resulting in what is now known as the Routh – Hurwitz theorem.

Stability, of course, is always present: the controller must ensure that the closed-loop system is stable, regardless of the open-loop stability.

A poor choice of controller can even worsen the stability of the open-loop system, which must normally be avoided.

# Chemical stability: CSF flows throughout the inner ventricular system in the brain and is absorbed back into the bloodstream, rinsing the metabolic waste from the central nervous system through the blood – brain barrier.

The primary benefit of running a driver in user mode is improved stability, since a poorly written user mode device driver cannot crash the system by overwriting kernel memory.

Its duties have expanded over the years, and today, according to official Federal Reserve documentation, include conducting the nation's monetary policy, supervising and regulating banking institutions, maintaining the stability of the financial system and providing financial services to depository institutions, the U. S. government, and foreign official institutions.

Today the Federal Reserve System has broader responsibilities than only ensuring the stability of the financial system.

* To maintain the stability of the financial system and contain systemic risk in financial markets

Dangerous characteristics such as stalling, spinning and pilot-induced oscillation ( PIO ), which depend mainly on the stability and structure of the aircraft concerned rather than the control system itself, can still occur with these systems.

Partly due to the lower overall weight of the system components ; and partly because the natural stability of the aircraft can be relaxed, slightly for a transport aircraft and more for a maneuverable fighter, which means that the stability surfaces that are part of the aircraft structure can therefore be made smaller.

Abdur Rahman's reforms of the army, legal system and structure of government were able to give Afghanistan a degree of unity and stability which it had not before known.

Rotation support implies the average circular motion of stars in the disk is responsible for the stability of the galaxy.

A larger metacentric height implies greater initial stability against overturning.

In other words, the just-world hypothesis is the tendency to attribute consequences to, or expect consequences as the result of, an unspecified power that restores moral balance ; the fallacy is that this implies ( often unintentionally ) the existence of such a power in terms of some cosmic force of justice, desert, stability, or order in the universe.

Higher degree of hollowness in the blade implies a thinner cross section and this affects the stability ( bending or buckling properties ) of the blade ; the thinner the blade the more flexible it is.

Some techniques ( notably conventional Fabry – Pérot detectors ) require high frequency stability and this usually implies long coherence length.