  We theoretically describe the behavior of a terahertz nano-oscillator based
on an anisotropic antiferromagnetic dynamical element driven by spin torque. We
consider the situation when the polarization of the spin-current is
perpendicular to the external magnetic field applied along the anisotropy
easy-axis. We determine the domain of the parametric space (field, current)
where the oscillator demonstrates chaotic dynamics. Characteristics of the
chaotic regimes are analyzed using conventional techniques such as spectra of
the Lyapunov exponents. We show that the threshold current of the chaos
appearance is particularly low in the vicinity of the spin-flop transition. In
this regime, we consider the mechanism of the chaos appearance in detail when
the field is fixed and the current density increases. We show that the
appearance of chaos is preceded by a regime of quasiperiodic dynamics on the
surface of a two-frequency torus arising in phase space as a result of the
Neimark-Sacker bifurcation.
