  We explore the nature of orbits of stars moving in the meridional plane
$(R,z)$ of an axially symmetric galactic model with a disk, a spherical
nucleus, and a flat biaxial dark matter halo component. In particular, we study
the influence of all the involved parameters of the dynamical system, by
computing both the percentage of chaotic orbits and the percentages of orbits
of the main regular resonant families in each case. To distinguish between
ordered and chaotic motion, we use the smaller alignment index (SALI) method to
extensive samples of orbits by numerically integrating the equations of motion
as well as the variational equations. Moreover, a method based on the concept
of spectral dynamics that utilizes the Fourier transform of the time series of
each coordinate is used to identify the various families of regular orbits and
also to recognize the secondary resonances that bifurcate from them. Two cases
are studied for every parameter: (i) the case where the halo component is
prolate and (ii) the case where an oblate dark halo is present. Our numerical
investigation indicates that all the dynamical quantities affect, more or less,
the overall orbital structure. It was observed that the mass of the nucleus,
the halo flattening parameter, the scale length of the halo, the angular
momentum, and the orbital energy are the most influential quantities, while the
effect of all the other parameters is much weaker. It was also found that all
the parameters corresponding to the disk only have a minor influence on the
nature of orbits. Furthermore, some other quantities, such as the minimum
distance to the origin, the horizontal, and the vertical force, were tested as
potential chaos detectors. Our analysis revealed that only general information
can be obtained from these quantities. We also compared our results with early
related work.
