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.
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