Three-Dimensional Discrete Echo-Memristor Map: Dynamic Analysis and DSP Implementation

Siqi Ding, Ke Meng, Minghui Zhang, Yiting Lin, Chunpeng Wang (), Qi Li (), Suo Gao and Jun Mou
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Siqi Ding: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
Ke Meng: School of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034, China
Minghui Zhang: School of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034, China
Yiting Lin: Guangdong Provincial/Zhuhai Key Laboratory of Interdisciplinary Research and Application for Data Science, Beijing Normal-Hong Kong Baptist University, Zhuhai 519087, China
Chunpeng Wang: Key Laboratory of Computing Power Network and Information Security, Ministry of Education, National Supercomputer Center in Jinan, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
Qi Li: Key Laboratory of Computing Power Network and Information Security, Ministry of Education, National Supercomputer Center in Jinan, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
Suo Gao: School of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034, China
Jun Mou: School of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034, China

Mathematics, 2025, vol. 13, issue 21, 1-16

Abstract: In recent years, with the development of novel hardware such as memristors, integrating chaotic systems with hardware implementations has enabled efficient and controllable generation of chaotic signals, providing new avenues for both theoretical research and engineering applications. In this work, we propose a novel memristor-based chaotic system, named the three-dimensional discrete echo-memristor map (3D-DEMM). The 3D-DEMM is capable of generating complex dynamic behaviors with self-similar attractor structures; specifically, under different parameters and initial conditions, the system produces similar attractor shapes at different amplitudes, which we refer to as an echo chaotic map. By incorporating the discrete nonlinear characteristics of memristors, the 3D-DEMM is systematically designed. We first conduct a thorough dynamic analysis of the 3D-DEMM, including attractor visualization, Lyapunov exponents, and NIST tests, to verify its chaoticity and self-similarity. Subsequently, the attractors of the 3D-DEMM are captured on a DSP platform, demonstrating discrete-time hardware simulation and real-time operation. Experimental results show that the proposed system not only exhibits highly controllable chaotic behavior but also demonstrates strong robustness in maintaining amplitude-invariant attractor shapes, providing a new theoretical and practical approach for memristor-based chaotic signal generation and applications in information security.

Keywords: memristor; chaotic system; self-similar attractor; DSP implementation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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