Wu Qiujie, Zhang Fanghai, Hong Qinghui, Wang Xiaoping, Zeng Zhigang
School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, 430074 China.
Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan, 430074 China.
Cogn Neurodyn. 2021 Feb;15(1):157-167. doi: 10.1007/s11571-020-09583-9. Epub 2020 Mar 19.
In order to overcome the security weakness of the discrete chaotic sequence caused by small Lyapunov exponent and keyspace, a general chaotic construction method by cascading multiple high-dimensional isomorphic maps is presented in this paper. Compared with the original map, the parameter space of the resulting chaotic map is enlarged many times. Moreover, the cascaded system has larger chaotic domain and bigger Lyapunov exponents with proper parameters. In order to evaluate the effectiveness of the presented method, the generalized 3-D Hénon map is utilized as an example to analyze the dynamical behaviors under various cascade modes. Diverse maps are obtained by cascading 3-D Hénon maps with different parameters or different permutations. It is worth noting that some new dynamical behaviors, such as coexisting attractors and hyperchaotic attractors are also discovered in cascaded systems. Finally, an application of image encryption is delivered to demonstrate the excellent performance of the obtained chaotic sequences.
为了克服离散混沌序列因小Lyapunov指数和密钥空间而产生的安全弱点，本文提出了一种通过级联多个高维同构映射的通用混沌构造方法。与原始映射相比，所得混沌映射的参数空间扩大了许多倍。此外，级联系统在适当参数下具有更大的混沌域和更大的Lyapunov指数。为了评估所提方法的有效性，以广义3-D Hénon映射为例分析了各种级联模式下的动力学行为。通过级联具有不同参数或不同排列的3-D Hénon映射获得了多样的映射。值得注意的是，在级联系统中还发现了一些新的动力学行为，如共存吸引子和超混沌吸引子。最后，给出了图像加密应用以证明所获得混沌序列的优异性能。
