  We develop a theoretical framework that allows us to explore the coupled
motion of neutron-superfluid vortices and proton-superconductor flux tubes in a
gravitationally collapsed condensate, which describe neutron stars that form
pulsars. Our framework uses the 3D Gross-Pitaevskii-Poisson-Equation (GPPE) for
neutron Cooper pairs, the Real-Time-Ginzburg-Landau equation (RTGLE) for proton
Cooper pairs, the Maxwell equations for the vector potential ${\bf A}$, and
Newtonian gravity and interactions, both direct and induced by the Poisson
equation, between the neutron and proton subsystems. For a pulsar we include a
crust potential, characterized by an angle $\theta$, and frictional drag. By
carrying out extensive direct numerical simulations, we obtain a variety of
interesting results. We show that a rotating proton superconductor generates a
uniform London magnetic field, which changes the field distribution inside flux
tubes. In the absence of any direct interaction between the two species, they
interact through the gravitational Poisson equation. The presence of attractive
(repulsive) density-density interaction leads to the attraction (repulsion)
between neutron vortices and proton flux tubes. The inclusion of the
current-current interaction and the complete Maxwell equations allows us to
quantify the entrainment effect that leads to induced magnetization of neutron
vortices. We show that, with a strong external magnetic field ${\bf B}_{\rm
ext}$, proton flux tubes are anchored to the crust, whereas neutron vortices
leave the condensate and lead to abrupt changes of the crust angular momentum
${\rm J}_c$. The frictional term in the dynamical equation for $\theta$ yields
stick-slip dynamics that leads, in turn, to glitches in the time series of
${\rm J}_c$. By calculating various statistical properties of this time series,
we demonstrate that they display self-organised criticality(SOC).
