We experimentally report the cyclic scenario of birth and annihilation of periodic orbits in a photonic integrated circuit as the feedback phase of the electric field varies. The latter is also shown to result in minimal alterations in the statistical properties of the chaotic attractor, with simultaneously transiting the Hurst exponent H , erratically, below and above the critical value of H=0.5 that indicates regular Brownian motion. Consequently there is an indication of the most effective operating regions with minimized predictability, which hinders eavesdropping and the progress of forecasting the development of the chaotic light carrier.