In this problem, you'll look at the nonlinear system
(dx)/(dt)=y-2-x
(dy)/(dt)=x^(2)-y
(a) Do a qualitative phase plane analysis of the system. That is, sketch all nullclines, and clearly
indicate the equilibrium points of the system. Use arrows to give the orientation on nullclines, as
well as in each region.
Note: Make your picture really big, as you'll be drawing on it more in the next part.
(b) This system has two equilibrium points. For each equilibrium point, find the eigenvalues of the
Jacobian. If the eigenvalues are real, also find the eigenvectors. Use this information to sketch
approximate trajectories near each equilibrium point on your picture from (a).
(c) Is each equilibrium point stable or not?
1.
In this problem,you'll look at the nonlinear system
(dx =y-2-x dt dy dt
a) Do a qualitative phase plane analysis of the system. That is, sketch all nullclines, and clearly indicate the equilibrium points of the system. Use arrows to give the orientation on nullclines, as well as in each region.
Note: Make your picture really big, as you'll be drawing on it more in the next part.
(b) This system has two equilibrium points. For each equilibrium point, find the eigenvalues of the Jacobian. If the eigenvalues are real, also find the eigenvectors. Use this information to sketch approximate trajectories near each equilibrium point on your picture from (a).
(c) Is each equilibrium point stable or not?