Assignment:
The predator prey system below has a term for the carrying capacity of the prey species. Initially the prey population N(0) = 330 and the predator population P(0) = 270.
dN/dt = 0.07N(700-N) - 0.05NP
dP/dt = 0.04PN - 4P
(a) In the absence of predators, what is the carrying capacity of the prey's environment?
(b) Use a step size of delta(t) = 0.05 and Euler's method, to model the population numbers over the next 5 years.
(c) i) Plot prey and predator population versus time on one graph.
ii) Plot prey population size versus predator population size.
iii) Do the results suggest a stable situation develops in time?
Provide complete and step by step solution for the question and show calculations and use formulas.