Question: Plotting bifurcation diagram for linear system with 2 equations and 1 parameter

I have the following system

pendsys := { diff(x(t),t) = a * x(t) + y(t), diff(y(t),t) = -x(t) + a * y(t) }:

with critical point being (0,0). After plotting the phase portrait, I found out that (0,0) is (asymptotically) stable when a<0 and unstable when a>0. Also, (0,0) is a center when a = 0. Also, as initial condition, I have x(0)=0, y(0)=1. I was thinking we have Hopf bifurcation at a = 0. My question is, how do I plot the bifurcation diagram for this system?

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