Consider the following first-order autonomous system $$ \begin{align} &\dot{x}=y,\\ &\dot{y}=-x^2+\mu, \end{align} $$ where $\mu$ is a parameter. When $\mu>0$, the system has two equilibrium points $x_1=\sqrt{\mu}$ and $x_2=-\sqrt{\mu}$. By considering the linearization the system around the equilibrium points, it is easy to check that $x_1$ is a center, while $x_2$ is a saddle point. The two equlibrium points collide at the bifurcation point $\mu=0$ and then disappear. What is this type of bifurcation called? It seems that this bifurcation is similar to the saddle-node bifurcation, but not exactly the same. Can anyone give some references?
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