Question 1- Find the (2, 2)-entry of the Jacobian matrix of the function
![1884_Figure.png](https://secure.tutorsglobe.com/CMSImages/1884_Figure.png)
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
![1702_Figure1.png](https://secure.tutorsglobe.com/CMSImages/1702_Figure1.png)
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.