Study of multiple time-scale dynamics in an optoelectronic feedback delay oscillator with piecewise linear transfer functions

In this paper, we investigate multiple time-scale oscillations in an optoelectronic feedback delay oscillator characterized by piecewise linear transfer functions. This system generates various microwave waveforms like square, triangular, sawtooth, complex and chaotic signals crucial for communications, radar, and metrology. In this study, we aim to present a method that can help us to understand the emergence of both slow and fast dynamics. Our study indicates that limit cycles and mixed-mode oscillations arise, respectively, as a result of Hopf bifurcation and the system’s low and fast time scales. The system displays a combination of mixed-mode oscillations and chaotic oscillations that arise from a series of period doubling cascades. The Hopf bifurcation parameters are identified through the use of bifurcation diagrams and asymptotic approximation techniques. To compute the system’s period, an analytical approximation method is used. As a result, the experimental observation of mixed-mode oscillations and chaotic waveforms in the system supports the theoretical analysis.