  We report using Clarke's concept of generalised differential and a
modification of Floquet theory to non-smooth oscillations, the occurrence of
discontinuity induced Hopf bifurcations and Neimark-Sacker bifurcations leading
to quasiperiodic attractors in a memristive Murali-Lakshmanan-Chua (memristive
MLC) circuit. The above bifurcations arise because of the fact that a
memristive MLC circuit is basically a nonsmooth system by virtue of having a
memristive element as its nonlinearity. The switching and modulating properties
of the memristor which we have considered endow the circuit with two
discontinuity boundaries and multiple equilibrium points as well. As the
Jacobian matrices about these equilibrium points are non-invertible, they are
non-hyperbolic, some of these admit local bifurcations as well. Consequently
when these equilibrium points are perturbed, they lose their stability giving
rise to quasiperiodic orbits. The numerical simulations carried out by
incorporating proper discontinuity mappings (DMs), such as the Poincar\'{e}
discontinuity map (PDM) and zero time discontinuity map (ZDM), are found to
agree well with experimental observations.
