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Math Help - Rearranging recurrance relation into logistic form

  1. #1
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    Rearranging recurrance relation into logistic form

    Hi, this is probably simple for most but I'm a little puzzled.

    Say I have a recurrence system

    P_0=50

    P_n+1 - P_n=(0.45 + 0.005P_n)P_n (n=0,1,2,3....)

    and I want to put it in logistic form

    rP_n(1 - P_n/E)

    where r and E are positive parameters

    Both examples I have are of the form (a - bP_n)P_n which means I get the 1 -, but now my logistic form is going to be 1 +, does this matter??

    Apologies if this is the wrong forum but it seemed quite general.
    Also sorry if this is a boneheaded question.
    Last edited by CaptainBlack; January 6th 2011 at 06:27 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Turlock View Post
    Hi, this is probably simple for most but I'm a little puzzled.

    Say I have a recurrence system

    P_0=50

    P_n+1 - P_n=(0.45 + 0.005P_n)P_n (n=0,1,2,3....)

    and I want to put it in logistic form

    rP_n(1 - P_n/E)

    where r and E are positive parameters

    Both examples I have are of the form (a - bP_n)P_n which means I get the 1 -, but now my logistic form is going to be 1 +, does this matter??

    Apologies if this is the wrong forum but it seemed quite general.
    Also sorry if this is a boneheaded question.
    There is something wrong with your problem, it cannot be transformed into a logistic equation (that is if you want a positive attarctor)

    CB
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    There is something wrong with your problem, it cannot be transformed into a logistic equation (that is if you want a positive attarctor)

    CB
    Hi. It's for an assignment question so I thought it was frowned upon to use the exact values when asking for help.

    My recurrance relation is (0.27 + 0.0009P_n)P_n
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Turlock View Post
    Hi. It's for an assignment question so I thought it was frowned upon to use the exact values when asking for help.

    My recurrance relation is (0.27 + 0.0009P_n)P_n
    It is not the exact values that are the problem but the "+" inside the brackets, when the other P_n term is brought over you have P_{n+1}=(1.27+0.0009*P_n)P_n, and so if P_n>0 we have P_{n+1}>1.27 P_n, so the sequence grows without bound.

    CB
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  5. #5
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    Ok, I think I've found my school boy error. I've got birth rate is 4.18 and death rate is 3.91+0.0009P. So obviously births minus deaths makes my P coefficient now minus. All the other times I had the P in the birth rate and it was already minus.

    Thanks for looking. I'm now suitably embarrassed.

    Much appreciated.
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