MCS 471 Computer Project 6

Due: Monday, July 20, 1998 in class. No extensions!

A classical model used to study interacting populations is the Volterra-Lotka or predator-prey model. Let x(t) be the population of the prey and y(t) be number of predator. The dynamics of the population is described by the system of differential equations: 

         x' =  a x - b x y,     x(0) = 80

         y' = -c y + d x y,     y(0) = 30

where    a = 0.25,  b = 0.01,  c = 1.0  and  d = 0.01.
  1. Use Euler's method with h = 0.4 ( n=200) and h = 0.1 ( n= 800) to approximate the solution. Graphically display the results in the phase plane (x,y).
  2. Use dsolve with the numeric option to constuct the solution for t in [0,80] and graphically display the results.
  3. Write a discussion comparing the results.
  4. By eliminating the t varlable, derive and graph an implicit solution f(x,y) in the phase plane (x,y). What special properties, if any, does the graph of this solution reveal? What further conclusions can you make about the numerical approximations.
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