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  2. Instability - Wikipedia

    en.wikipedia.org/wiki/Instability

    In dynamical systems instability means that some of the outputs or internal states increase with time, without bounds. [1] Not all systems that are not stable are unstable; systems can also be marginally stable or exhibit limit cycle behavior.

  3. Stability theory - Wikipedia

    en.wikipedia.org/wiki/Stability_theory

    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.

  4. Hydrodynamic stability - Wikipedia

    en.wikipedia.org/wiki/Hydrodynamic_stability

    The presence of colloid particles (typically with size in the range between 1 nanometer and 1 micron), uniformly dispersed in a binary liquid mixtures, is able to drive a convective hydrodynamic instability even though the system is initially in a condition of stable gravitational equilibrium (hence opposite to the Rayleigh-Taylor instability ...

  5. Structural stability - Wikipedia

    en.wikipedia.org/wiki/Structural_stability

    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 .

  6. Chetaev instability theorem - Wikipedia

    en.wikipedia.org/wiki/Chetaev_instability_theorem

    The Chetaev instability theorem for dynamical systems states that if there exists, for the system ˙ = with an equilibrium point at the origin, a continuously differentiable function V(x) such that the origin is a boundary point of the set G = { x ∣ V ( x ) > 0 } {\displaystyle G=\{\mathbf {x} \mid V(\mathbf {x} )>0\}} ;

  7. Stability - Wikipedia

    en.wikipedia.org/wiki/Stability

    Chemical stability, occurring when a substance is in a dynamic chemical equilibrium with its environment Thermal stability of a chemical compound; Kinetic stability of a chemical compound; Stability constants of complexes, in solution; Convective instability, a fluid dynamics condition

  8. Dynamical systems theory - Wikipedia

    en.wikipedia.org/wiki/Dynamical_systems_theory

    In sports biomechanics, dynamical systems theory has emerged in the movement sciences as a viable framework for modeling athletic performance and efficiency. It comes as no surprise, since dynamical systems theory has its roots in Analytical mechanics. From psychophysiological perspective, the human movement system is a highly intricate network ...

  9. Nyquist stability criterion - Wikipedia

    en.wikipedia.org/wiki/Nyquist_stability_criterion

    The Nyquist plot for () = + + with s = jω.. In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker [] at Siemens in 1930 [1] [2] [3] and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, [4] is a graphical technique ...