https://nemenmanlab.org/~ilya/index.php?action=history&feed=atom&title=Physics_380%2C_2011%3A_Lecture_22Physics 380, 2011: Lecture 22 - Revision history2026-05-17T09:40:06ZRevision history for this page on the wikiMediaWiki 1.31.0https://nemenmanlab.org/~ilya/index.php?title=Physics_380,_2011:_Lecture_22&diff=349&oldid=prevIlya: 1 revision imported2018-07-04T16:28:42Z<p>1 revision imported</p>
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</td></tr></table>Ilyahttps://nemenmanlab.org/~ilya/index.php?title=Physics_380,_2011:_Lecture_22&diff=348&oldid=prevnemenman>Ilya: /* Main lecture */2011-11-15T14:36:35Z<p><span dir="auto"><span class="autocomment">Main lecture</span></span></p>
<p><b>New page</b></p><div>{{PHYS380-2011}}<br />
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We are continuing our short introduction to dynamical systems.<br />
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==Main lecture==<br />
#Once systems become more than 1d, other arrangements but fixed points are possible. One may have oscillations as well. Consider a system of two interacting genes: <math>\begin{array}{l}\frac{dX}{dt}=C_X+\frac{V_X}{1+(Y/K_Y)^2}-rX \\ \frac{dY}{dt}=C_Y +\frac{V_Y X^2}{1+(X/K_X)^2}-rY\end{array}</math>.<br />
#*The point of zero derivatives are: for X: <math>X=\left(C_X+\frac{V_X}{1+(Y/K_Y)^2}\right)/r</math>, and for Y, <math>Y=\left(C_Y +\frac{V_Y X^2}{1+(X/K_X)^2}\right)/r</math>.</div>nemenman>Ilya