There are initially 500 rabbits (x) and 200 foxes (y) on Farmer Oat's property. Use Polymath or MATLAB to plot the concentration of foxes and rabbits as a function of time for a period of up to 500 days. The predator-prey relationships are given by the following set of coupled ordinary differential equations: dx/dt = k-1 x - k_2 x .y
dy/dt = k_3 x. y y - k_4 y
Constant for growth of rabbits k_1 = 0.02 day6-1
Constant for death of rabbits k_2 = 0.00004/(day x no. of foxes)
Constant for growth of foxes after eating rabbits k_3 = 0.0004/(day x no. of rabbits)
Constant for death of foxes k_4 = 0.04 day^-1
What do your results look like for the case of k_3 = 0.00004/(day x no. of rabbits) and t_final = 800 days? Also plot the number of foxes versus the number of rabbits. Explain why the curves look the way they do