Question 1- Find the (2, 2)-entry of the Jacobian matrix of the function
At the point (2, 1).
Question 2- Consider the nonlinear system
x' = 12 - 0.1xy - 0.3
y' = 0.1xy - 2y
in the region x, y ≥ 0
a) Draw the x-and y-nullclines.
b) Identify all equilibria.
c) Sketch the phase portrait.
Question 3- Consider a disease that propagates according to the system
dx/dy = 16 - 0.2xy - 0.4x
dy/dx = 0.1xy - 8y
where x represented susceptible individuals, y represented infected individuals
a) Find all biologically meaningful steady states.
b) Show that the Jacobian matrix of this system is given by
c) For the biologically meaningful steady from (a), find the eigenvalues of the Jacobian matrix.
d) Determine the stability of the biologically meaningful steady states.