Chapter 9.4, Problem 15P

(a)

To determine

To sketch: The nullclines and describe how the critical points move as $\alpha$ increases.

(b)

To determine

The critical points using the given data.

(c)

To determine

The corresponding linear system for each critical point at $\alpha =2$ and phase portrait figure in a rectangle containing critical points.

(d)

To determine

The bifurcation point ${\alpha }_0$ at which the critical point coincides and eigenvalues of the corresponding linear system and a phase portrait.

(e)

To determine

To draw: A phase portrait by choosing a value $\alpha >{\alpha }_0$.