Hopf bifurcation and limit cycles

$$dV/dt=10(V-\frac{V^3}{3}-R+I_{input})$$ $$dR/dt=0.8(-R+1.25V+1.5)$$

Use $I_{input}$ as the relative parameter to prove that there these equations undergo 2 hopf bifurcations and indicate whether each is subcritical or supercritical.

Setting both equal to 0 to find the equilibrium:

$0=V-\frac{V^3}{3}-R+I_{input}$

$0=R+1.25V+1.5$

I guess I don't really know how to continue from here.. find eigenvalues?

jacobian (not sure if I computed this correctly): \begin{array}{lcr} \mbox1-v^2 & -1 \\ \mbox1.25 & -1 \\ \end{array}

So I know that a supercritical hopf bifurcation is a stable LC around an unstable equilibrium and a subcritical hopf bifurcation is a an unstable LC around a stable equilibrium.

• Why would someone downvote this question..? – Math Major Nov 14 '14 at 17:53
• Is $I_{input}$ a constant or time varying? – Amzoti Nov 14 '14 at 21:46