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Synchronization between the spatial Julia sets of complex Lorenz system and complex Henon map

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Abstract

In this paper, the definition of Julia set of complex Lorenz system is introduced. By using two different nonlinear coupling methods, the different structure synchronization between the Julia sets of complex Lorenz system and Henon map is investigated. In the former method, the synchronization is realized by adjusting a single coupling parameter. In order to quantify the synchronization process with the changing coupling parameter, a mathematical approach is proposed. The later method constructs a novel coupling term by replacing the coupling parameter with a coupling matrix. Through choosing a proper coupling matrix, the synchronization is also achieved. Numerical simulations verify the effectiveness of the methods.

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Acknowledgments

The research is supported by the National Nature Science Foundation of China (numbers 61273088, 10971120) and the Nature Science Foundation of Shandong province (number ZR2010FM010). The authors would like to thank the editors and anonymous referees for their constructive comments and suggestions.

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  1. College of Control Science and Engineering, Shandong University, Jinan, 250061, People’s Republic China

    Da Wang & ShuTang Liu

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  1. Da Wang
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  2. ShuTang Liu
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Correspondence to ShuTang Liu.

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Wang, D., Liu, S. Synchronization between the spatial Julia sets of complex Lorenz system and complex Henon map. Nonlinear Dyn 81, 1197–1205 (2015). https://doi.org/10.1007/s11071-015-2061-x

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