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Predator prey model

  1. May 6, 2009 #1
    1. The problem statement, all variables and given/known data
    x'=x(1+2x-x2-y)
    y'=y(x-a)



    I need help finding the equilibrium points of this system.
     
  2. jcsd
  3. May 6, 2009 #2
    What part are you confused about?
     
  4. May 6, 2009 #3
    well let me state the entire problem:

    Consider the predator prey type of system that's given above with a>0. The population x is prey. By itself, its rate of growth increases for small populations and then decreases for x>1. The predator is given by y, and it dies out when no prey is present. The parameter is given by a. You are asked to show that this system has a Hopf bifurcation.
    i) Find the fixed point (xa,ya) with both xa,ya positive.
     
  5. May 6, 2009 #4
    Can xa or ya be 0?
     
  6. May 6, 2009 #5
    It doesn't say anything about that. And as a matter of fact, I was getting (0,0) as one of my equilibrium points.
     
  7. May 6, 2009 #6
    (0,0) is an equilibrium point. Another one occures when x = 0, a 3rd one occurs when y = 0. To find the 4th equilibrium point, solve 1+2x-x2-y and x - a simultaneously.
     
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