Reference no: EM132216969

Question: Sketch the bifurcation diagram of the following ODE for x ∈ R

dx/dt = -μ² - x³ + ∈x

on varying μ, considering the cases ∈ > 0, ∈ = 0 and ∈ < 0. Be careful to indicate the stability of any branches and verify that there are saddle-node bifurcations for ∈ > 0. Verify for μ = ∈ = 0 that there is an equilibrium at x = 0 that is neither linearly stable nor unstable (this is called an Isola bifurcation). Show that the curve of saddle-node bifurcations in the (μ, ∈) plane is 9μ² = 2√(3∈^3/2) and plot this curve.