Recursive synchronization of the unified chaotic system using a single time series

This paper investigates the application of a recursive synchronization technique that can be applied to chaotic systems, using a single time series. The Unified system is used to exemplify the chaotic systems due to its versatile characteristics. The proposed method doesn't require the direct construction of an error signal between the measurable state and its estimate; thus, allowing for easily constructing a reduced-order state observer. Proving the stability of the synchronization mechanism is done using a systematic Lyapunov-based approach. Adjusting the decay rates of the synchronization errors is achieved by tuning of the proposed observation gains of the system. It is demonstrated that different sets of gains can be chosen to achieve a stable satisfactory performance, which is an added advantage to the proposed system. Different scenarios that include the Lorenz, the Lü, and the Chen systems are explored to provide a rich comparison between the proposed system and other synchronization techniques, reported in the literature. Extensions, improvements, and possible real-world applications are also discussed to complete the analysis of the recursive nature of the proposed system.