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 May 8th, 2017, 05:32 PM #1 Newbie   Joined: Mar 2015 From: Penns Posts: 8 Thanks: 0 Markov Chain Discrete Dynamical System Hey guys, so my teacher told us to look at the book and find a very similar problem and to just do it. I don't typically ask for the answer but I just need help setting up this problem. A drug is administered @ 100 units of the drug into the blood. Every 10 minutes, 50% of the drug goes to bloodstream & 50% to liver During this same time period 75% of the drug in the liver goes to the bloodstream while 25% stays in the liver. Initially injection gets process started 100 units of the drug directly to blood stream(0 to liver). How to model this system given x sub k = amount in blood stream after 10 min time interval. y sub k = amount of drug in the liver after k 10 min time intervals have passed. Using matrix algebra: X(k+1) = A * X(k)[X is a vector] where X(k)= Matrix x sub k over y sub k. Then there is another matrix showing A = (2x2) matrix top 2 values are 1/2 & 3/4. Bottom 2 values are 1/2 and 1/4. Can any one tell me what the hell is going on? I think I can use the markov chain or the matrix algebra. I'm super lost and a step by step is appreciated. May 8th, 2017, 05:56 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,631 Thanks: 1470 if I understand this what you have is $\begin{bmatrix}b_{n+1} \\l_{n+1}\end{bmatrix}=\begin{bmatrix}0.5 &0.75\\0.5 &0.25\end{bmatrix}\begin{bmatrix}b_n \\ l_n\end{bmatrix}$ $\begin{bmatrix}b_0 \\ l_0\end{bmatrix}=\begin{bmatrix}100 \\ 0\end{bmatrix}$ May 8th, 2017, 06:35 PM   #3
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 Originally Posted by romsek if I understand this what you have is $\begin{bmatrix}b_{n+1} \\l_{n+1}\end{bmatrix}=\begin{bmatrix}0.5 &0.75\\0.5 &0.25\end{bmatrix}\begin{bmatrix}b_n \\ l_n\end{bmatrix}$ $\begin{bmatrix}b_0 \\ l_0\end{bmatrix}=\begin{bmatrix}100 \\ 0\end{bmatrix}$

That is correct. It's a bit confusing saying find all the eigen values & bases for all eigenspaces of the matrix A. I get eigen-values and all. But it's confusing in the form of a word problem. I think you help me set it up tho. Tags chain, discrete, dynamical, markov, system Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post eric_h22 Differential Equations 0 March 31st, 2015 07:08 AM kfp22 Advanced Statistics 0 October 8th, 2014 07:43 AM butabi Advanced Statistics 1 February 12th, 2012 04:20 PM agsmith87 Real Analysis 0 February 9th, 2012 09:02 PM alpacino Applied Math 0 April 26th, 2009 07:48 AM

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