Question: For each problem, determine equilibrium points, bifurcation points, and construct a bifurcation diagram. Discuss the different behaviors in each system. a. (y^{prime}=y-mu y^{2}) b. (y^{prime}=y(mu-y)(mu-2

For each problem, determine equilibrium points, bifurcation points, and construct a bifurcation diagram. Discuss the different behaviors in each system.

a. $y^{\prime}=y-\mu y^{2}$

b. $y^{\prime}=y(\mu-y)(\mu-2 y)$

c. $x^{\prime}=\mu-x^{3}$

d. $x^{\prime}=x-\frac{\mu x}{1+x^{2}}$

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