Question

the following EDO:
dx/dt= x⁴ −µx²
where µ is a parameter in R.

(i) Identify the critical value fµ_C or which a bifurcation occurs. Give the equilibrium points for µ <µ_C and µ> µ_C, say if each of these is stable or unstable, and plot the phase lines for these two cases.

(ii) Draw the bifurcation diagram indicating in dotted line the unstable equilibrium points and in solid line the stable equilibrium points.

Answer 1