沈阳工业大学学报2025，Vol.47Issue(5)：602-608,7.DOI:10.7688/j.issn.1000-1646.2025.05.07
五维混沌系统的切换幅值控制
Switching amplitude control of five-dimensional chaotic system
摘要
Abstract
[Objective]Due to the influence of the limited regulated direct current(DC)power supply,amplitude control of each variable of the chaotic system,that is,variable compression,has become an essential prerequisite for chaotic circuit design and implementation.Currently,geometric control of the attractors of chaotic systems,such as amplitude control and bias control,is a hot research direction in the field of chaotic systems.Based on existing methods,a new amplitude control method was proposed in this paper in the expectation of exploring more potential applications of chaotic systems.[Methods]A five-dimensional chaotic system was developed,and its chaos was verified by using a three-dimensional phase diagram and Lyapunov exponents.After the absolute values of state variable-u in the two equations of the system were taken,two new switched chaotic systems were obtained.Compared with the phase diagram of the chaotic system,the amplitudes of these two new systems changed,and their shapes were highly similar,namely that global amplitude control was achieved.After the absolute value of-u in the second equation was taken,it became a memristive chaotic system.The existence of the memristor was verified by the pinched hysteresis loops of three frequencies.Further analysis of the memristive chaotic system was carried out.By adding the parameter k to the three nonlinear terms of the memristive chaotic system,it was found that the average amplitudes of the attractor on five dimensions changed accordingly,which indicated that the memristive chaotic system had a global amplitude control parameter.The existence of multi-stability in the memristive chaotic system was verified by the Lyapunov exponent spectrum changed with the memristive parameter a.Moreover,the absolute mean value of the signal and the phase diagram changed with a proved that when an appropriate value of the memristive parameter a was selected,global amplitude control could also be achieved.[Results]The simulation circuit equations,equivalent circuit diagram of the memristive chaotic system,and the simulated phase diagram of the chaotic system on the oscilloscope are highly similar to the computer simulation results,which indicates that the chaotic circuit design is of reliability.[Conclusion]The proposed five-dimensional chaotic system has strong chaotic property.The switching system with switching amplitude variation was proposed,providing a new direction for the research of memristive chaotic systems.In future work,it is possible to attempt to use a curved surface as the switching surface.Additionally,through computer simulation experiments,whether the phenomenon of switching amplitude variation widely exists in memristive chaotic systems will be further studied,and further work will be carried out to explore the principle of its existence.The phase diagram on the oscilloscope is highly consistent with the computer simulation experiment in five dimensions.The system has the characteristics of high dimensionality,strong chaos,and switching amplitude control,which make it have good application prospects in engineering.关键词
混沌/忆阻器/切换混沌系统/相图/李雅普诺夫指数/信号均值/全局调幅/电路实现Key words
chaos/memristor/switched chaotic system/phase diagram/Lyapunov exponent/mean value of signal/global amplitude control/circuit implementation分类
信息技术与安全科学引用本文复制引用
郑莉,魏君..五维混沌系统的切换幅值控制[J].沈阳工业大学学报,2025,47(5):602-608,7.基金项目
辽宁省教育厅基础研究项目(lnjc202018). （lnjc202018）
