  We report emergence of saturation and chaotic spiking of optical power in a
double ring resonator with balanced loss and gain, obeying the so-called
parity-time symmetry. We have modeled the system using a discrete-time
iterative equation known as the Ikeda Map. In the linear regime, evolution of
optical power in the system shows power saturation behavior below the PT
threshold and exponential blow-up above the PT threshold. We found that in the
unbroken PT regime, optical power saturation occurs owing to the existence of
stable stationary states, which lies on the surface of 4-dimensional
hypersphere. Inclusion of Kerr nonlinearity into our model leads to the
emergence of a stable, chaotic and divergent region in the parameter basin for
period-1 cycle. A closer inspection into the system shows us that the largest
Lyapunov exponent blows up in the divergent region. It is found that the
existence of high non-negative largest Lyapunov exponent causes chaotic spiking
of optical power in the resonators.
