**Abstract:** The model of a memristor-based oscillator with cubic nonlinearity is studied. The considered system has infinitely many equilibrium points, which build a line of equilibria in the phase space. Numerical modeling of the dynamics is combined with the bifurcational analysis. It has been shown that the oscillation excitation has distinctive features of the supercritical Andronov-Hopf bifurcation and can be achieved by changing of a parameter value as well as by variation of initial conditions. Therefore, the considered bifurcation is called Andronov-Hopf bifurcation with and without parameter.