b) The equation TA = EA -gA3 - KA is said to undergo a transcritical bifurcation when g = 0; this case is the borderline between supercritical and subcritical bifurcation. Find the relation between A* and c when g = 0. c) In experiments on Taylor Couette vortex flow, Aitta et al. (1985)" were able to change the parameter g continuously from positive to negative by varying the aspect ratio of their experimental set-up. Assuming that the equation is modified to dA dt =h+ EA -943 - KA5, (9.0.3) where h > 0 is a slight imperfection, sketch the bifurcation diagram of A* versus c in the three cases: g >0, g =0, and g