Plot bifurcation diagrams for the planar systems (a) r = r( 0.2r6 + r4 r2),

Plot bifurcation diagrams for the planar systems

(a) ˙r = r(μ − 0.2r6 + r4 − r2), ˙ θ = −1,

(b) ˙r = r((r − 1)2 − μr), ˙ θ = 1.

Give a possible explanation as to why the type of bifurcation in part (b)

should be known as a fold bifurcation.