Fast time-reversible synchronization of chaotic systems

Synchronization of nonlinear systems is a crucial problem in many applications, including system identification, data forecasting, compressive sensing, coupled oscillator topologies, and neuromorphic systems. Despite many efficient synchronization techniques being developed, there are some unresolved issues such as fast and reliable synchronization using short or noisy fragments of available data. In this paper, we use time-reversible integration to obtain a synchronization technique as a generalization of the well-known Pecora-Carroll method. The proposed time-symmetric synchronization technique employs the time reversibility of a discrete system obtained by the symmetric integration method. This approach allows the complete synchronization of two chaotic systems using minimal, sparse, or noisy sync data from one state variable without any controller. An example of rapid unidirectional time-symmetric synchronization of several test chaotic systems is shown to verify the performance of the proposed technique. We show that the time-reversible approach works for both conservative and dissipative systems, but highly depends on initial conditions. To increase the overall performance of the time-symmetric synchronization scheme, we suggest using a computationally simple and easy-to-implement time-reversible semi-implicit numerical integration method. Several possible applications include chaos-based communications, chaotic signal filtering, and systems based on coupled oscillators.