Consider the equation $$\dot{x} = \mu x$$.
The origin is stable for $\mu < 0$ and unstable for $\mu>0$. Is there a name for this bifurcation?
2026-03-25 20:36:36.1774470996
What is the name of the bifurcation with normal form $\dot{x} = \mu x$?
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I don't think that there is a name for this kind of bifurcation. Generally, Bifurcation theory is used for nonlinear differential equations. Your equation is a simple linear equation. This implies that the stability of the system is global and the system is actually pretty uninteresting :D. For $\mu>0$ we have an unstable system (I can say system because the system is linear). For $\mu=0$ we have a system with infinitely many equilibrium points. And For $\mu <0$ we have exponential asymptotic stability.