  We demonstrate how the pitchfork, transcritical and saddle-node bifurcations
of steady states observed in dynamical systems with a finite number of isolated
equilibrium points occur in systems with lines of equilibria. The exploration
is carried out by using the numerical simulation and linear stability analysis
applied to a model of a memristor-based oscillator. First, all the discussed
bifurcation scenarios are considered in the context of systems including Chua's
memristor with a piecewise-smooth characteristic. Then the memristor
characteristic is changed to a function that is smooth everywhere. Finally, the
action of the memristor forgetting effect is taken into consideration. The
presented results are obtained for electronic circuit models, but the
considered bifurcation phenomena can be exhibited by systems with a line of
equilibria of any nature.
