  This paper investigates dynamics of axial reflection symmetric model in
self-interacting Brans-Dicke gravity for anisotropic fluid. We formulate
hydrodynamical equations and discuss oscillations using time-dependent
perturbation for both spin as well as spin-independent cases. The expressions
of frequency, total energy density and equation of motion of oscillating model
are obtained. We study instability of oscillating models in weak
approximations. It is found that the oscillations and stability of the model
depend upon the dark energy source along with anisotropy and reflection
effects. We conclude that the axial reflection system remains stable for
stiffness parameter $\Gamma=1$, collapses for $\Gamma>1$ and becomes unstable
for $0<\Gamma<1$.
