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Equilibrium points

  1. May 6, 2007 #1


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    1. The problem statement, all variables and given/known data

    Given the system

    (a) Find the equilibria of the system.
    (b) Choose any positive a,b,c,d. Start close to each equilibrium and find the solution numerically.

    3. The attempt at a solution

    (a) Solving for x and y in the system, the equilibrium points are x(t)=y(t)=0 and x(t)=c/d, y(t)=a/b.

    (b) Choose a=c=0.6 and b=d=0.3. Then the equilibrium points are (x,y)=(0,0) and (x,y)=(2,2). I wrote a fortran program to solve the equations using euler's method, but the values I got back didn't make sense. I figure this is because I am incorrectly choosing the initial values of x and y.

    When it says "start close to each equilibrium", does this mean I should choose the initial values of x and y to be something like 0.1 and 2.1? In part (c) I need to graph the solutions so any quick help is appreciated!

    Also, this is the program I am using:

    REAL*4 T,X,Y,H
    DIMENSION T(11), X(11), Y(11)
    T(1) = 0
    X(1) = 0.1
    Y(1) = 0.1
    H = 1
    DO 1, I=1,11
    T(I+1) = T(I) + H
    X(I+1) = X(I) + H*(0.6*X(I)-0.3*X(I)*Y(I))
    Y(I+1) = Y(I) + H*(0.3*X(I)*Y(I)-0.6*Y(I))
    WRITE(*,100) (T(I),X(I),Y(I), I=1,11)
    100 FORMAT(1x,3(D24.14))
  2. jcsd
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