Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity

Lijuan Chen, Mingchu Yu, Jinnan Luo (), Jinpeng Mi, Kaibo Shi and Song Tang
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Lijuan Chen: Kaiserslautern Intelligent Manufacturing School, Shanghai Dianji University, Shanghai 201306, China
Mingchu Yu: Kaiserslautern Intelligent Manufacturing School, Shanghai Dianji University, Shanghai 201306, China
Jinnan Luo: College of Electrical Engineering, Southwest Minzu University, Chengdu 610041, China
Jinpeng Mi: TAMS Group, Department of Informatics, Universität Hamburg, 20148 Hamburg, Germany
Kaibo Shi: School of Information Science and Engineering, Chengdu University, Chengdu 610106, China
Song Tang: TAMS Group, Department of Informatics, Universität Hamburg, 20148 Hamburg, Germany

Mathematics, 2024, vol. 12, issue 12, 1-17

Abstract: Chaotic or hyperchaotic systems have a significant role in engineering applications such as cryptography and secure communication, serving as primary signal generators. To ensure stronger complexity, memristors with sufficient nonlinearity are commonly incorporated into the system, suffering a limitation on the physical implementation. In this paper, we propose a new four-dimensional (4D) hyperchaotic system based on the linear memristor which is the most straightforward to implement physically. Through numerical studies, we initially demonstrate that the proposed system exhibits robust hyperchaotic behaviors under typical parameter conditions. Subsequently, we theoretically prove the existence of solid hyperchaos by combining the topological horseshoe theory with computer-assisted research. Finally, we present the realization of the proposed hyperchaotic system using an FPGA platform. This proposed system possesses two key properties. Firstly, this work suggests that the simplest memristor can also induce strong nonlinear behaviors, offering a new perspective for constructing memristive systems. Secondly, compared to existing systems, our system not only has the largest Kaplan-Yorke dimension, but also has clear advantages in areas related to engineering applications, such as the parameter range and signal bandwidth, indicating promising potential in engineering applications.

Keywords: hyperchaotic system; linear memristor; strong complexity; topological horseshoe; FPGA implementation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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