Results 1 to 2 of 2

Math Help - ricker, beverton-holt models

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    13

    ricker, beverton-holt models

    Ricker model
    \frac{dN}{dt}=\frac{rN}{e^{\beta N}}

    Beverton-Holt model
    \frac{dN}{dt}=\frac{rN}{\alpha +N}

    To get steady states, do I just set \frac{dN}{dt}=0 for both models?
    I'm not sure how to get stability. Do I just take the derivative of both models and plug in the steady states?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ezong View Post
    Ricker model
    \frac{dN}{dt}=\frac{rN}{e^{\beta N}}

    Beverton-Holt model
    \frac{dN}{dt}=\frac{rN}{\alpha +N}

    To get steady states, do I just set \frac{dN}{dt}=0 for both models?
    I'm not sure how to get stability. Do I just take the derivative of both models and plug in the steady states?
    Linearise about the steady state and either solve the linearised equation, if you have a growing solution you have instability. Alternativly just examin the linearised equation to determine the stability of the steady state.

    In these cases the steady state appears to be N=0, and for a small departure from the steady state the departure grows if r>0 and r/\alpha>0 respectivly.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Holt-Winter and Box-Jenkins Examples?
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: November 16th 2011, 04:03 PM
  2. Logistic Models
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: May 5th 2010, 03:15 AM
  3. Quadratic models
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 22nd 2008, 10:28 PM
  4. models
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: February 17th 2008, 05:19 PM
  5. Replies: 2
    Last Post: July 17th 2007, 06:11 AM

Search Tags


/mathhelpforum @mathhelpforum