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(Solved): Draw a bifurcation diagram for the \( \mathrm{ODE} \) \[ \frac{d y}{d t}=\mu+\frac{1}{2} y-\frac{y ...



Draw a bifurcation diagram for the \( \mathrm{ODE} \)
\[
\frac{d y}{d t}=\mu+\frac{1}{2} y-\frac{y}{1+y}
\]
for the parameter

Draw a bifurcation diagram for the \( \mathrm{ODE} \) \[ \frac{d y}{d t}=\mu+\frac{1}{2} y-\frac{y}{1+y} \] for the parameter range \( -3 \leq \mu \leq 3 \) and include representative phase lines at the values \( \mu=-2 \), \( \mu=-1, \mu=0, \mu=1 \), and \( \mu=2 \) and at any bifurcation value. Identify any bifurcation point(s) [meaning find the \( \mu \) and \( y \) value] exactly (use calculus and algebra, and don't just estimate a numerical value base on a graph). Label the bifurcation points(s) on your bifurcation diagram.


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The phase line diagram has a close relative called a bifurcation diagram. The purpose of the diagram is to display qualitative information about equil
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