Two-dimensional memristive hyperchaotic maps with different coupling frames and its hardware implementation

Mengjiao Wang; Mingyu An; Shaobo He; Xinan Zhang; Herbert Ho-Ching Iu; Zhijun Li

doi:10.1063/5.0154516

Two-dimensional memristive hyperchaotic maps with different coupling frames and its hardware implementation

Chaos. 2023 Jul 1;33(7):073129. doi: 10.1063/5.0154516.

Authors

Mengjiao Wang¹, Mingyu An¹, Shaobo He¹, Xinan Zhang², Herbert Ho-Ching Iu², Zhijun Li¹

Affiliations

¹ School of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, China.
² School of Electrical, Electronic and Computer Engineering, University of Western Australia, Crawley, WA 6009, Australia.

PMID: 37459221
DOI: 10.1063/5.0154516

Abstract

Continuous-time memristors have been used in numerous chaotic circuit systems. Similarly, the discrete memristor model applied to a discrete map is also worthy of further study. To this end, this paper first proposes a discrete memristor model and analyzes the voltage-current characteristics of the memristor. Also, the discrete memristor is coupled with a one-dimensional (1D) sine chaotic map through different coupling frameworks, and two different two-dimensional (2D) chaotic map models are generated. Due to the presence of linear fixed points, the stability of the 2D memristor-coupled chaotic map depends on the choice of control parameters and initial states. The dynamic behavior of the chaotic map under different coupled map frameworks is investigated by using various analytical methods, and the results show that different coupling frameworks can produce different complex dynamical behaviors for memristor chaotic maps. The dynamic behavior based on parameter control is also investigated. The numerical experimental results show that the change of parameters can not only enrich the dynamic behavior of a chaotic map, but also increase the complexity of the memristor-coupled sine map. In addition, a simple encryption algorithm is designed based on the memristor chaotic map under the new coupling framework, and the performance analysis shows that the algorithm has a strong ability of image encryption. Finally, the numerical results are verified by hardware experiments.