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Complex function projective synchronization of complex chaotic system and its applications in secure communication

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Abstract

To develop secure communication, the paper presents complex function projective synchronization (CFPS) of complex chaotic systems. Aimed to coupled complex chaotic system, the control law is derived to make the complex state vectors asymptotically synchronize up to a desired complex function matrix. Based on CFPS, a novel communication scheme is further designed in theory. Its main idea is chaotic masking in essence, but the transmitted signal is the derivative of the product of the information signal and chaotic signal. As the complex scaling functions are arbitrary and more unpredictable than real scaling functions, and the product and derivative operations of complex numbers are complicated, the possibility that an interceptor extracts the information from the transmitted signal is greatly reduced. The communication system can transmit analog signal and digital symbols with fast transmission and high security, especially low bit-error rate and the strong robustness to noise for digital symbols. The corresponding numerical simulations are performed to verify and illustrate the analytical results.

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Acknowledgments

The work was partially supported by the National Nature Science Foundation of China (numbers 61273088, 10971120, 61001099) and the Nature Science Foundation of Shandong province (number ZR2010FM010). The authors would like to thank the editors and the reviewers for their constructive comments and suggestions which improved the quality of the paper.

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  1. College of Control Science and Engineering, Shandong University, No. 17923 Jingshi Road, Jinan , 250061, China

    Shutang Liu & Fangfang Zhang

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  1. Shutang Liu
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  2. Fangfang Zhang
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Correspondence to Fangfang Zhang.

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Liu, S., Zhang, F. Complex function projective synchronization of complex chaotic system and its applications in secure communication. Nonlinear Dyn 76, 1087–1097 (2014). https://doi.org/10.1007/s11071-013-1192-1

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