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State Vectors

  1. Jun 9, 2008 #1
    1. The problem statement, all variables and given/known data
    In order to prodice a more balanced, sustainable long term mix of flower Skwhere the percentage of the offspring of red flowers are p pink and 1-p redSk= A SoSk= [r p w]Twhere A=[1-p* 1/4* 0p***** 1/2* 1/20***** 1/4* 1/2]determine the stady state eigenvectors(you do not have to solve the characteristic equation, but can assume there is an eigenvalue of 1).If the breeder wants the long term steady state to have twice as many red flowers as pink, what should p be?

    2. Relevant equations
    Sk+1=A*SkSk= b1([tex]\lambda[/tex]1)^k[X1] +b2([tex]\lambda[/tex]2)^k [X2] +b3([tex]\lambda[/tex]3)^k [X3]
    [b1 b2 b3]T= P^(-1)*So

    3. The attempt at a solution

    okay i assumed the [tex]\lambda[/tex]1 =1 was dominant because when
    [tex]\lambda[/tex]<1 the proportion of the population will become extinct and when
    [tex]\lambda[/tex]>1 the proportion of the population has a very very large number
    this was just so i can find my steady state eigenvector but i still dont knwo how to find that.

    so Sk=b1 [X1]

    Im not sure how to go about this but I tried finding Pinverse using 1/detA[adjA]
    and i came out with something ugly like:
    Pinverse=8/1-2p * [1/8 1/8 1/8
    .........................1/2p 1/2-1/2p 1/2-1/2p
    .........................1/4p 1/4-1/4p 1/2-3/4p]

    but i realize I dont know what to do after this and I do not think it helps to solve the problem at all

    could anyone please help me out in finding the steady state eigenvector? once i figure that out ill be able to get the final answer
    all i know is that the answer is 1/8=0.125=p
    Last edited: Jun 9, 2008
  2. jcsd
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