There are initially 500 rabbits (x) and 200 foxes (y) on Farmer Oat’s property near Riça, Jofostan. 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= k1x-k2x. Y
dy/dt= k3x. Y-k4y
Constant for growth of rabbits k1 = 0. 02
Constant for death of rabbits k2 = 0. 00004/(day × no. Of foxes)
Constant for growth of foxes after eating rabbits k3 = 0. 0004/(day × no. Of rabbits)
Constant for death of foxes k4 = 0. 04 What do your results look like for the case of k3 = 0. 00004/(day × no. Of rabbits) and tfinal = 800 days?
Also, plot the number of foxes versus the number of rabbits. Explain why the curves look