Revealing the network of periodic orbits in galaxy models with a prolate
  or an oblate dark matter halo component
  Locating the position of periodic orbits in galaxies is undoubtedly an issue
of paramount importance. We reveal the position and the stability of periodic
orbits of stars moving in the meridional plane $(R,z)$ of an axially symmetric
galactic model with a disk, a spherical nucleus, and a biaxial dark matter halo
component. In particular, we study how all the involved parameters of the
dynamical system influence the position and the stability of all resonant
families. To locate the position and measure the stability of periodic orbits
we use a highly sensitive numerical code which is able to identify resonant
periodic orbits of the type $n:m$. Two cases are studied for every parameter:
(i) the case where the dark matter halo component is prolate and (ii) the case
where an oblate dark matter halo is present. Our numerical exploration reveals
that all the dynamical quantities affect, more or less, the position and the
stability of the periodic orbits. It is shown that the mass of the nucleus, the
mass of the disk, the halo flattening parameter, the scale length of the halo,
the angular momentum, and the total orbital energy are the most influential
quantities, while the effect of all other parameters is much weaker.
