Physics 380, 2011: Lecture 22

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Back to Physics 380, 2011: Information Processing in Biology.

We are continuing our short introduction to dynamical systems.

Main lecture

1. 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: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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}} .
   • The point of zero derivatives are: for X: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X=\left(C_X+\frac{V_X}{1+(Y/K_Y)^2}\right)/r} , and for Y, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Y=\left(C_Y +\frac{V_Y X^2}{1+(X/K_X)^2}\right)/r} .