Consider the Lotka-Volterra competition model presented in class,
where Ni is the density of competing species i.
(a) What are nullclines of N1 and N2?
(b) What are equilibria of N1 and N2?
(c) Show the parameter condition in which an internal equilibrium is stable.
(d) Show the Jacobian matrix of the model.
(e) Calculate the Jacobian matrix of the model at the internal equilibrium.
(f) When r1 = r2 = 1,α11 = α22 = 1, and α12 = α21 = 0.5, calculate eigenvalues and eigenvectors.
(g) Explain the difference between the eigenvectors and nullclines.
