Consider the following model,
dx
dt = x2y −x + ay,
dy
dt = b −ay −x2y,
where x and y are concentrations of chemical substances.
(a) What are nullclines of x and y?
(b) What are equilibria of x and y?
(c) Show the Jacobian matrix of the model.
(d) Calculate the Jacobian matrix of the model at an internal equilibrium .
(e) Calculate the trace and determinant of the Jacobian matrix at the internal
equilibrium.
(f) Show the parameter condition in which the internal equilibrium is unstable.
