Different Dimension Synchronization of Bidirectionally Coupled Chaotic Systems With Unknown Time‐Varying Parameter Interference

In this paper, the synchronization issue of bidirectionally coupled chaotic systems with unknown time‐varying parameter interference across different dimensions is explored. Specifically, scale matrices are meticulously designed to tackle the synchronization problem of chaotic systems in two distinct dimensions. Meanwhile, the technique of variable congelation is employed to handle the aforementioned unknown time‐varying parameter interference. Based on the Lyapunov stability theorem, the synchronization controllers in different dimensions are obtained. At the same time, adaptive laws of the unknown interference can be designed. Benefiting from the proposed methods, it is verified that regardless of whether it occurs in three‐dimensional (3D) or four‐dimensional (4D) synchronization, all synchronization errors can be globally uniformly ultimately bounded as time tends to infinity. Moreover, it is ensured that both control and estimation signals remain bounded. Eventually, simulation studies based on two financial systems are conducted to validate the effectiveness of the proposed synchronization method.