Assignment:
The population sizes of a prey, X, and a predator, Y (measured in thousands) are given by x and y, respectively. They are governed by the differential equations
? = −pxy + qx and ? = rxy - sy (where p, q, r and s are positive constants (p ≠ r).
In the absence of species Y (i.e. y = 0), how would I ?nd a solution for x at time t if x(0) = x0, where x0 > 0. Is this model realistic? Why?
- How to determine all the equilibrium points for this system of di?erential equations expressing my answer in terms of p, q, r and s.
- How to classify each equilibrium point using the method of matrices with two real distinct eigenvalues?
Provide complete and step by step solution for the question and show calculations and use formulas.