Time-Reversible Synchronization of Analog and Digital Chaotic Systems

The synchronization of chaotic systems is a fundamental phenomenon in nonlinear dynamics. Most known synchronization techniques suggest that the trajectories of coupled systems converge at an exponential rate. However, this requires transferring a substantial data array to achieve complete synchronization between the master and slave oscillators. A recently developed approach, called time-reversible synchronization, has been shown to accelerate the convergence of trajectories. This approach is based on the special properties of time-symmetric integration. This technique allows for achieving the complete synchronization of discrete chaotic systems at a superexponential rate. However, the validity of time-reversible synchronization between discrete and continuous systems has remained unproven. In the current study, we expand the applicability of fast time-reversible synchronization to a case of digital and analog chaotic systems. A circuit implementation of the Sprott Case B was taken as an analog chaotic oscillator. Given that real physical systems possess more complicated dynamics than simplified models, analog system reidentification was performed to achieve a reasonable relevance between a discrete model and the circuit. The result of this study provides strong experimental evidence of fast time-reversible synchronization between analog and digital chaotic systems. This finding opens broad possibilities in reconstructing the phase dynamics of partially observed chaotic systems. Utilizing minimal datasets in such possible applications as chaotic communication, sensing, and system identification is a notable development of this research.