Open AccessResearch on cascading high-dimensional isomorphic chaotic maps
Author(s) -
Qiujie Wu,
Fanghai Zhang,
Qinghui Hong,
Xiaoping Wang
Publication year - 2020
Publication title -
cognitive neurodynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.83
H-Index - 41
eISSN - 1871-4099
pISSN - 1871-4080
DOI - 10.1007/s11571-020-09583-9
Subject(s) - chaotic , lyapunov exponent , attractor , encryption , sequence (biology) , coupled map lattice , cascade , computer science , dynamical systems theory , topology (electrical circuits) , domain (mathematical analysis) , chaotic map , hénon map , statistical physics , mathematics , algorithm , synchronization of chaos , control theory (sociology) , mathematical analysis , artificial intelligence , physics , control (management) , combinatorics , chemistry , chromatography , quantum mechanics , biology , genetics , operating system
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.