Consider the equationdy/dt = ay y3 = y(a y2). (iii)(a)

Chapter 2, Problem 26

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Consider the equationdy/dt = ay y3 = y(a y2). (iii)(a) Again consider the cases a < 0, a = 0, and a > 0. In each case find the critical points,draw the phase line, and determine whether each critical point is asymptotically stable,semistable, or unstable.(b) In each case sketch several solutions of Eq. (iii) in the ty-plane.(c) Draw the bifurcation diagram for Eq. (iii)that is, plot the location of the criticalpoints versus a. For Eq. (iii) the bifurcation point at a = 0 is called a pitchfork bifurcation.Your diagram may suggest why this name is appropriate.