| The theory of complex dynamic system flourished with the rise of nonlinear science and computer technology in the mid-20th century. Complex value chaotic system is the extension of real value chaotic system,and is a kind of typical complex dynamic system. At present,the influence of the complex dynamic system has been deep into the information security,financial analysis, biology, and other fields, and it shows a broad prospect of application. The existence of the complex variable is a significant sign of complex chaotic systems. The complex variable can be unfolded into real part and imaginary part and the complex chaotic system has more complex dynamic behaviors, which increase the amount of information in the secure communications and increase the communication security. In order to further understand complex chaotic systems' characteristics and application prospect, this paper shows a series research of the dynamic behaviors, synchronous control method and application schemes of complex chaotic systems, mainly including the simplifiy method of complex chaotic system, improved synchronization control idea, and application in secret communication, image encryption, the FPGA digital implementation.Firstly,a class of complex chaotic systems' dynamic behaviors and simplified method were proposed. An obvious proportional relation in the complex variable was found from the analysis of complex Lorenz system, complex Chen system and complex Lu system, and k is used to describe the relationship with analysis. Then proposed a simplified method,by which the complex Lorenz system has been simplified. Through the simplified system,the dynamic behaviors of the complex Lorenz system can be well seen by simulation. Finally a simplified law was proposed,and the simplified systems of fractional complex Lorenz system,complex Chen system, complex Lu system and hyper complex Lu system are given to verify the proposed law.Secondly, an improved synchronization control method for complex value chaotic system was proposed based on the simplified method. It can be used to simplify the design of synchronization system,in which the drive system is the complex value chaotic system which can be simplified. As a contrast, the generalized projective synchronization between complex Lorenz system and Lorenz system was realized by two methods, one is the traditional and another is the improved. The result of simulation proved that the new proposed method is effectively.Thirdly, the design and its application in secure communication and image encryption of a new complex Lorenz-like system with varying parameter were given. A new Lorenz-like system and complex Lorenz-like system was proposed by adding a state feedback function,and then a synchronization system between the two systems was reached based on the simplified method. This synchronization system is driven by only one complex variable, and based on the synchronization system a chaotic parameter modulation digital secure communication system is given. Finally a three-order image encryption algorithm is also given and the encryption and decryption of "Lena" are realized with analysis.Finally, the digital implementation of complex Lu system on FPGA was given. The digital implementation of complex Lu system is realized based on the simplified method and the FPGA exploitation board. With the help of DA chips, the curves and phase diagram of complex Lu system can be seen on oscilloscope, which show a good performance of the designed system with with low resource consumption. |
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