Question

This problem focuses on using Polymath, an ordinary differential equation (ODE) solver, and also a non-linear equation (NLE) solver.
(a) 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\cdot y
{dy}/{dt}=k_{3}x-k_{4}x\cdot y
Constant for growth of rabbits k1 = 0.02 day-1
Constant for death of rabbits k1 = 0.00004 / (dayx no. of foxes)
Constant for growth of foxes after eating rabbits k1 = 0.0004 / (dayx no. of rabbits)
Constant for death of foxes k1 = 0.04 day-1
What do your results look like for the case of k3 = 0.00004 / (day x no. of rabbits) and tfinal = 800 days? Also, plot the number of foxes versus the number of rabbits. Explain why the curves look the way they do. Vary the parameter k1, k2, k3, and k4. Discuss which parameter can or cannot be larger than others. Write a paragraph describing what you find.
(b) Use Polymath or MATLAB to solve the following set of nonlinear algebraic equations:
x^{3}y-4y^{2}+3x=1
6y^{2}-9xy=5
with initial guess of x = 2, y = 2.

Answer 1

Answer:

here

Step-by-step explanation: