一类四维忆阻混沌电路的动力学行为分析

doi:10.19596/j.cnki.1001-246x.7678

计算物理 ›› 2018, Vol. 35 ›› Issue (4): 458-468.DOI: 10.19596/j.cnki.1001-246x.7678

一类四维忆阻混沌电路的动力学行为分析

刘娣¹, 杨芳艳², 周国鹏³, 李清都², 廖晓昕⁴

1. 东南大学网络空间安全学院, 南京 210096;
2. 重庆邮电大学自动化学院, 重庆 400065;
3. 湖北科技学院工程技术研究院, 湖北咸宁 437100;
4. 华中科技大学自动化学院, 湖北武汉 430074

收稿日期:2017-04-24 修回日期:2017-07-12 出版日期:2018-07-25 发布日期:2018-07-25
作者简介:刘娣(1989-),女,硕士研究生,研究方向:混沌电路设计与仿真,非线性动力学,E-mail:liud923@126.com
基金资助:
国家自然科学基金（61501073，71473073），NSFC-浙江两化融合联合基金（U1509217），湖北省科技支撑计划项目（2015BAA001）及湖北省中小企业创新基金（2015DAL069）资助项目

Dynamical Behavior Analysis of a Class of 4D Memristive Chaotic System

LIU Di¹, YANG Fangyan², ZHOU Guopeng³, LI Qingdu², LIAO Xiaoxin⁴

1. School of Cybersecurity, Southeast University, Nanjing 210096, China;
2. School of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
3. Research Institute of Engineering Technology, Hubei University of Science and Technology, Xianning Hubei 437100, China;
4. School of Automation, Huazhong University of Science and Technology, Wuhan Hubei 430074, China

Received:2017-04-24 Revised:2017-07-12 Online:2018-07-25 Published:2018-07-25

摘要/Abstract

摘要： 讨论一类4D忆阻混沌电路的动力学行为，并研究多稳定性的吸引域.为保证计算结果的高效性和准确性，利用CPU+GPU的大规模计算能力和具有128位小数的多精度GMP库及MPFR库，计算出对应吸引子的吸引域，并用区间牛顿法验证当吸引域很小时吸引子的存在性；最后运用拓扑马蹄理论和构造忆阻模拟电路两种方式验证系统超混沌的存在性.

关键词: 4D忆阻混沌电路, 多稳定性, 吸引域, 拓扑马蹄, 超混沌

Abstract: Dynamical behavior of a class of 4D memristive chaotic circuits was discussed, and attracting domain of multi-stability was studied. In order to guarantee efficiency and accuracy of calculation results, CPU+GPU large-scale computing power were introduced and more than 128 decimal places of precision GMP library and MPFR library were applied to calculate domain of corresponding attractor. Finally, existence of hyperchaos was proved by using method of topological horseshoe theory and constructing memristive analog circuit.

Key words: 4D memristive chaotic system, multi-stability, attracting domain, topological horse shoe, hyperchaos

中图分类号:

刘娣, 杨芳艳, 周国鹏, 李清都, 廖晓昕. 一类四维忆阻混沌电路的动力学行为分析[J]. 计算物理, 2018, 35(4): 458-468.

LIU Di, YANG Fangyan, ZHOU Guopeng, LI Qingdu, LIAO Xiaoxin. Dynamical Behavior Analysis of a Class of 4D Memristive Chaotic System[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(4): 458-468.

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一类四维忆阻混沌电路的动力学行为分析

Dynamical Behavior Analysis of a Class of 4D Memristive Chaotic System

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