Consider the second order nonlinear differential equation x ′′(t) + x ′ (t) − µx(t) + x 3 (t) = 0, where µ ∈ R. (a) Rewrite the above equation as a system of first order equations (in matrix form) and find all the equilibrium (critical) points of the resulting system.
 (b) Obtain the eigenvalues of the corresponding linear system, in terms of µ, at each equilibrium point.  (c) In each case classify the systems equilibrium (critical) points in terms of its type and stability (or instability) and identify the bifurcation values for the system.  (ii) Determine the type of bifurcation that occurs for the following systems: (a) dx dt = rx − x 2 , dy dt = x − y,  (b) dx dt = rx − x 3 , dy dt = −y.  Confirm your analytical results with qualitatively different phase portraits before and after the bifurcation point. If instructed, draw the bifurcation diagram as well as the phase portraits by using Matlab.