{i} Plot the bifurcation diagram [such that the implicit solution of f{a,y} = {1, which describes the set of equilibrium points for a given parameter r1; see above) for g = a- 3:2}- in the rectangle - 2 6: r1 -:: 2.. - 2 c: y .-:_ 2. Based on your results in Exercise 2.. explain which of the branches in the bifurcation diagram belong to asymptotically stable or unstable equilibrium points of the autonomous differential equation. (Hint: nmnpycoutour has some issues when determining roots when there is no sign change at the root. consider here instead the modified function fix-r11 y] = Hf\" HZ}, essentially removing one of the identical factors.) Remark: 'We see a Errcalled pitchfork bifurcation at a = {II due to the form of the bifurcation diagram, which resembles a pitchfor'n. {ii} For :1 = 1 the corresponding differential equation is d: :Tf = iil 3:2}- Verify using :15 I've from syrupy that the general solution in implicit form is given via 1 \"q f-'lii'lo _' llr=e_ r\" s 1 y y L; li.'.r together Plot the equilibrium solutions and the solution curves passing through pm] = [1.3 and mm] with the direct-ion eld of the differential equation in the rectangle 2 mi t c: H11 - 1'. :2 y c: 2