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Autonomous system (mathematics)
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{{Short description|System of ordinary differential equations whose current state solely determines its evolution}} [[File:Stability_Diagram.png|thumb|300px|[[Stability theory|Stability diagram]] classifying [[Poincaré map#Poincaré maps and stability analysis|Poincaré maps]] of linear '''autonomous system''' <math>x' = Ax,</math> as stable or unstable according to their features. Stability generally increases to the left of the diagram.<ref>[http://www.egwald.ca/linearalgebra/lineardifferentialequationsstabilityanalysis.php Egwald Mathematics - Linear Algebra: Systems of Linear Differential Equations: Linear Stability Analysis] Accessed 10 October 2019.</ref> Some sink, source or node are [[equilibrium point]]s.]] [[File:Phase plane nodes.svg|thumb|300px|2-dimensional case refers to [[Phase plane]].]] In [[mathematics]], an '''autonomous system''' or '''autonomous differential equation''' is a [[simultaneous equations|system]] of [[ordinary differential equation]]s which does not explicitly depend on the [[independent variable]]. When the variable is time, they are also called [[time-invariant system]]s. Many laws in [[physics]], where the independent variable is usually assumed to be [[time]], are expressed as autonomous systems because it is assumed the [[Physical law|laws of nature]] which hold now are identical to those for any point in the past or future.
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