A wide variety of phenomena can occur when an equilibrium point is completely degenerate,...

A wide variety of phenomena can occur when an equilibrium point is completely degenerate, i.e., when the Jacobian is the zero matrix. We will look at just one. Consider the system

a) Show that the Jacobian at the origin is the zero matrix.

b) Plot the solutions through the six points (0, ±1), and . Plot additional solutions of your choice.

c) Compare what you see with the behavior of solutions near a saddle point.