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
- 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 (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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}}}
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- The point of zero derivatives are: for X: Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle X=\left(C_{X}+{\frac {V_{X}}{1+(Y/K_{Y})^{2}}}\right)/r} , and for Y, Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle Y=\left(C_{Y}+{\frac {V_{Y}X^{2}}{1+(X/K_{X})^{2}}}\right)/r} .
