Stability: Difference between revisions

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|Meaning=#The characteristic of a system if sufficiently small disturbances have only small effects,  either decreasing in [[amplitude]] or oscillating periodically; it is asymptotically stable if the effect  of small disturbances vanishes for long time periods.
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|Explanation=A system that is not stable is referred to as unstable, for which small disturbances may lead to  large effects. Some authors also distinguish a neutral or marginally stable case, in which disturbances  do not vanish, but also do not grow without bound. Classically, stability was defined only with  respect to systems in [[equilibrium]]. More recently it has been extended to apply to evolving systems,  for which an unstable [[disturbance]] leads to an evolution that becomes uncorrelated with the  undisturbed evolution. From this standpoint stability and [[predictability]] can be equated.<br/>  
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#<br/>''Same as'' [[static stability]].<br/>  
== stability ==
#The property that each computed solution (in exact arithmetic) of a finite difference approximation  remains bounded for all possible choices of the time step.<br/> <br/>''See'' [[Lax equivalence theorem]].<br/>  
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#The ability of [[laminar flow]] to become turbulent in a fluid.
 
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#<div class="definition"><div class="short_definition">The characteristic of a system if sufficiently small disturbances have only small effects,  either decreasing in [[amplitude]] or oscillating periodically; it is asymptotically stable if the effect  of small disturbances vanishes for long time periods.</div><br/> <div class="paragraph">A system that is not stable is referred to as unstable, for which small disturbances may lead to  large effects. Some authors also distinguish a neutral or marginally stable case, in which disturbances  do not vanish, but also do not grow without bound. Classically, stability was defined only with  respect to systems in [[equilibrium]]. More recently it has been extended to apply to evolving systems,  for which an unstable [[disturbance]] leads to an evolution that becomes uncorrelated with the  undisturbed evolution. From this standpoint stability and [[predictability]] can be equated.</div><br/> </div>
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#<div class="definition"><div class="short_definition"><br/>''Same as'' [[static stability]].</div><br/> </div>
#<div class="definition"><div class="short_definition">The property that each computed solution (in exact arithmetic) of a finite difference approximation  remains bounded for all possible choices of the time step.</div><br/> <div class="paragraph"><br/>''See'' [[Lax equivalence theorem]].</div><br/> </div>
#<div class="definition"><div class="short_definition">The ability of [[laminar flow]] to become turbulent in a fluid.</div><br/> </div>
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Latest revision as of 06:59, 30 March 2024

  1. The characteristic of a system if sufficiently small disturbances have only small effects, either decreasing in amplitude or oscillating periodically; it is asymptotically stable if the effect of small disturbances vanishes for long time periods.

A system that is not stable is referred to as unstable, for which small disturbances may lead to large effects. Some authors also distinguish a neutral or marginally stable case, in which disturbances do not vanish, but also do not grow without bound. Classically, stability was defined only with respect to systems in equilibrium. More recently it has been extended to apply to evolving systems, for which an unstable disturbance leads to an evolution that becomes uncorrelated with the undisturbed evolution. From this standpoint stability and predictability can be equated.


  1. Same as static stability.
  2. The property that each computed solution (in exact arithmetic) of a finite difference approximation remains bounded for all possible choices of the time step.

    See Lax equivalence theorem.
  3. The ability of laminar flow to become turbulent in a fluid.
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