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In this paper, two scaling matrices are used to research the synchronization of different dimensional chaotic systems with unknown parameters. Firstly, the definition of synchronization of chaotic systems with different dimensions is introduced. Secondly, based on Lyapunov stability theorem and adaptive control method, an adaptive feedback hybrid controller and parameter adaptive laws are designed to realize synchronization of uncertain chaotic systems with different dimensions. Finally, three numerical experiments are carried out to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

It is an important to achieve the hybrid synchronization of the chaotic financial system. Chaos synchronization is equivalent to the error system which is asymptotically stable. The hybrid synchronization for a class of finance chaotic systems is discussed. First, a simple single variable controller is obtained to synchronize two identical chaotic financial systems with different initial conditions. Second, a novel algorithm is proposed to determine the variables of the master system that should antisynchronize with corresponding variables of the slave system and use this algorithm to determine the corresponding variables in the chaotic financial systems. The hybrid synchronization of the chaotic financial systems is realized by a simple controller. At the same time, different controllers can implement the chaotic financial system hybrid synchronization. In comparison with the existing results, the obtained controllers in this paper are simpler than those of the existing results. Finally, numerical simulations show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Based on a special matrix structure, the projective synchronization control laws of the hyperchaotic financial systems are proposed in this paper. Put a hyperchaotic financial system as the drive system, via transformation of the system state variables, construct its response system, and then design the controller based on the special matrix structure. The given scheme is applied to achieve projective synchronization of the different hyperchaotic financial systems. Numerical experiments demonstrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]