We consider a synthetic antiferromagnetic spin-torque oscillator with
anisotropic interlayer exchange coupling. This system exhibits exceptional
points in its linearized dynamics. We find the non-linear dynamics and the
dynamical phase diagram of the system both analytically and numerically.
Moreover, we show that, near one of the exceptional points, the power of the
oscillator depends extremely sensitively on the injected spin current. Our
findings may be useful for designing sensitive magnetometers and for other
applications of spin-torque oscillators.Comment: 7 pages, 4 figure