The next exercises are designed to test your ability to distinguish among the various types of bifurcations - it's easy to confuse them! In each case, find the values of $r$ at which bifurcations occur, and classify those as saddle-node, transcritical, supercritical pitchfork, or subcritical pitchfork. Finally, sketch the bifurcation diagram of fixed points $x^{*}$ vs. $r$. 3.4.5 $\quad \dot{x}=r-3 x^{2}$ 3.4.6 $\quad \dot{x}=r x-\frac{x}{1+x} $ 3.4.7 $\quad \dot{x}=5-r e^{-x^{2}}$ 3.4.8 $\quad \dot{x}=r x-\frac{x}{1+X^{2}}$ 3.4.9 $\quad \dot{x}=x+\tanh ( x) $ 3.4.10 $\quad \dot{x}=r x+\frac{x^{3}}{1+x^{2}}$ SP.AS3991