Dynamics of Time-Delayed Optoelectronic Oscillators With Nonlinear Amplifiers and Its Potential Application to Random Numbers Generation

Abstract

Time-delayed dynamical systems generally feature smooth nonlinear transfer functions in the feedback loop, such as polynomial or sinusoidal functions. As a consequence, the complexity of their dynamical behavior mainly originates from the time-delay. In this paper, we explore the opposite case where the nonlinear transfer function is complex ( cos <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (sinh)), and therefore, non-smooth. We perform a bifurcation analysis of the system, and evidence that this novel type of time-delayed system can display a chaotic behavior characterized by positive maximum Lyapunov exponent and quasi-maximal entropy. The high entropy behavior of the system combined with post-processing are used to generate random numbers for small values of the feedback gain with an overall bit rate up to 1.478 Gb/s. Our theoretical results are in excellent agreement with experimental measurements, performed with an optoelectronic oscillator involving a complex transfer function designed ad hoc.