For the canonical form of the transcritical bifurcation where u is a real parameter d dt x(t) = Mx = μx − x², determine the local stability of any equilibria, and sketch the bifurcation diagram. Next, consider the differential equation —y(t) = Ay² (1 − 2)y = ƒ (λ, y), dt where is a real parameter. Find the bifurcation point (y*, 2*), sketch the bifurcation diagram, and show that the differential equation for y is similar to the differential equation for x by Taylor expanding f(x,y).

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