Example 2.  Lotka-Volterra Model.  Solve the I.V.P.  
      with  ,  
and
      with  .    
Use several intervals  .
2 (a).  Use the interval   .
2 (b).  Use the interval   .
2 (c).  Use the interval   .
Can you discover if the solution form an "orbit."

Solution 2.

Enter the functions    and    and form the vector function  .  

Compute the Runge-Kutta solution.

Do the two curves join up?

The "true solution" is known to be a closed curve, and there is no known analytic formulas for the solution curve.  

More subintervals will produce better results.  

Aside.  

Let us investigate the critical point of the D. E.

(c) John H. Mathews 2004