https://en.formulasearchengine.com/api.php?action=feedcontributions&feedformat=atom&user=95.132.133.174formulasearchengine - User contributions [en]2026-06-08T21:37:59ZUser contributionsMediaWiki 1.43.0-wmf.28https://en.formulasearchengine.com/index.php?title=Dadda_multiplier&diff=12972Dadda multiplier2014-01-20T19:02:25Z<p>95.132.133.174: /* Algorithm example */</p>
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The '''Chetayev instability theorem''' for [[dynamical system]]s states that if there exists for the system <math>\dot{\textbf{x}} = X(\textbf{x})</math> a function V('''x''') such that<br />
# in any arbitrarily small neighborhood of the origin there is a region D<sub>1</sub> in which V('''x''') > 0 and on whose boundaries V('''x''') = 0;<br />
# at all points of the region in which V('''x''') > 0 the [[Total derivative|total time derivative]] <math>\dot{V}(\textbf{x})</math> assumes positive values along every trajectory of <math>\dot{\textbf{x}} = X(\textbf{x})</math><br />
# the origin is a [[Boundary (topology)|boundary point]] of D<sub>1</sub>;<br />
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then the trivial solution is unstable. <br />
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This theorem is somewhat less restrictive than the [[Lyapunov instability theorem]]s, since a complete sphere (circle) around the origin for which V and <math>\dot{V}</math> both are of the same sign does not have to be produced..<br />
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== See also ==<br />
* [[Chetayev Nikolay Gurievich]]<br />
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[[Category:Theorems in dynamical systems]]</div>95.132.133.174