1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Population model

  1. Sep 22, 2013 #1
    1. The problem statement, all variables and given/known data

    The simplest useful model for fisher comes from the logistic model for population growth, together with a harvest h which is proportional to the current population P, that is,


    where the constant E is called the effort. E measures the fraction of the population harvested, so that 0 <= E <= 1. This gives the model

    dP/dt = kP(1-(P/a) - EP,

    where P(t) is the number of these fish at time t year and k (the natural growth rate) and a( the carrying capacity) are constants for a particular fish polulation. In what follows take k= 1 and a= 4, for simplicity.

    a) determine the equilibrium solutions for a given effort E.

    my attempt.

    dP/dt = P - P^2/4 - EP

    dP/dt = ( P + E) (P -1/4)

    equilibrium solutions are when dP/dt=0

    so P(0)= -E, 1/4.
    Last edited: Sep 22, 2013
  2. jcsd
  3. Sep 23, 2013 #2


    User Avatar
    Homework Helper

    You miss a parentheses: dP/dt = kP(1-(P/a)) - EP

    The last equation is wrong.

    Because of the faulty factorisation, the result is not correct (and physically impossible).

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted