  We show the possibility of controlling the dynamical behavior of a single
fiber ring (SFR) resonator system with the fiber being an amplified (gain)
channel and the ring being attenuated (loss) nonlinear dielectric medium. Our
model is based on the simple alterations in the parity time symmetric synthetic
coupler structures proposed recently [A. Regensburger et al., Nature 488, 167
(2012)]. The system has been modeled using the transfer matrix formalism. We
find that this results in a dynamically controllable algorithm for the chaotic
dynamics inherent in the system. We have also shown the dependence of the
period doubling point on the input amplitude, emphasizing on the dynamical
aspects. Moreover, the fact that the resonator essentially plays the role of a
damped harmonic oscillator has been elucidated with the non-zero intensity
inside the resonator due to constant influx of input light.
