Bifurcations where eigenvalues become purely imaginary

Question

Say a system of 2 ODE's has the following Jacobian at a fixed point $(0,0)$, $$ Df_{\mu}(0,0) = \begin{pmatrix} -(1/2 - \mu) & 1/2+\mu \\ -(1/2 + \mu) & 1/2-\mu \end{pmatrix} $$ with eigenvalues $\lambda = \pm \sqrt{-2\mu}$. Clearly the eigenvalues are real and distinct for $\mu<0$, are both $0$ for $\mu=0$, and are complex conjugate for $\mu>0$. I've been searching for some references on such a bifurcation, which doesn't seem to resemble a Hopf bifurcation (where the real component of $\lambda$ is dependent on $\mu$, but not the imaginary component). Any recommendations or references would be greatly appreciated.