Results 1 to 2 of 2

Thread: population model, so confused

  1. #1
    May 2009

    population model, so confused

    Suppose that a population model is the logistic model with harvesting term h, a constant.


    r,h,alpha +ve constants

    1.)assume r>4h(alpha).find and classify the steady states N_1 and N_2 where N_1<N_2.

    I can find steady states of normal differential equations and sub in x=whatever when f(x)=0 but i dont have a clue what this is asking of me. any useful sites would be much appreciated also.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Mar 2009
    In general if dy/dx = f(y)

    Then the steady state solutions are the zeroes of f(y)

    Let a =alpha

    For dN/dt = rN(1-aN) - h

    Steady states are found when rN(1-aN) - h = 0

    Expanding -arN^2 + rN - h = 0

    Use the good ol' quadratic formula

    N = 1/2a + sqrt(r^2 - 4arh)/2ar

    this will clean up to 1/2a + sqrt(1-4ah/r)/2a

    or N = [1 + sqrt(1-4ah/r)]/2a

    since r > 4ah the solutions are real

    By considering a graph of dN/dt vs N you should be able to determine N1 unstable and N2 stable

    If you want see my web site :
    Last edited by Calculus26; Jun 9th 2009 at 05:56 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. logistic model for population
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: Oct 25th 2009, 06:55 AM
  2. Population model
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Feb 3rd 2009, 02:25 AM
  3. calculus - population model/de
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 11th 2008, 02:26 AM
  4. Population Model
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Sep 20th 2007, 05:55 AM
  5. population growth model
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Mar 27th 2006, 08:38 PM

Search Tags

/mathhelpforum @mathhelpforum