摘要
大范围混沌系统由于能提供更宽的混沌区间,常用于保密通信等领域,已有的大范围混沌系统多为三维和四维系统,为了得到混沌特性更强和更复杂的系统,本研究提出了一个具有大范围超混沌状态且能产生多种共存吸引子的五维系统。通过用共存分岔图、共存相轨图、Lyapunov指数谱以及计算系统散度等方法去分析该五维系统的动力学特性。结果表明:该系统是一个耗散的超混沌系统;参数固定时,仅改变初始值系统能产生多个共存吸引子,当参数d取不同的值时,该系统会产生12种类型的共存现象,分别为周期1、周期2、周期4、拟周期、一涡卷吸引子、双涡卷吸引子等相互共存;当参数m在[0.1,4000]区间变化时,该系统会一直保持超混沌状态,并且m在[70,4000]范围内,系统的Lyapunov指数谱保持不变且维持3个正Lyapunov指数的超混沌状态,说明了该系统具有不变Lyapunov指数特性。此外,用现场可编程门阵列(FPGA)进行数字电路实现,在示波器上观察实验结果,验证了该超混沌系统的可实现性。
Large-scale chaotic systems are often used in secure communication and other fields,because they can provide a wider chaotic interval.Most of the existing large-scale chaotic systems are three-dimensional and fourdimensional systems.In order to obtain more chaotic and more complex systems,this study proposed a fivedimensional system with a large range of hyperchaotic states and multiple coexisting attractors.The dynamic characteristics of the five-dimensional system were analyzed by means of coexistence bifurcation diagram,coexistence phase diagram,Lyapunov exponent spectrum and calculation of system divergence.The results show that:the system is a dissipative hyperchaotic system;when the parameters are fixed,the system can produce multiple coexisting attractors only by changing the initial value,and when the parameter d takes different values,the system will produce 12 types of coexistence phenomena,which are period-1 attractor,period-2 attractor,period-4 attractor,quasi-periodic attractor,one-scroll attractor,double-scroll attractor and so on;when the parameter m varies in the range of[0.1,4000],the system will always maintain a hyperchaotic state,and when m is in the range of[70,4000],the Lyapunov exponent spectrum of the system remains unchanged and maintains a hyperchaotic state with three positive Lyapunov exponents,indicating that the system has an invariant Lyapunov exponent characteristic.FPGA(field programmable gate array)was used to realize the digital circuit,and the experimental results were observed on the oscilloscope,which verified the feasibility of the hyperchaotic system.
作者
曾以成
李文轩
孙小力
ZENG Yicheng;LI Wenxuan;SUN Xiaoli(School of Physics and Optoelectronics,Xiangtan University,Xiangtan 411105,Hunan,China;Yanshan College,Shandong University of Finance and Economics,Jinan 250000,Shandong,China)
出处
《华南理工大学学报（自然科学版）》
EI
CSCD
北大核心
2024年第1期139-146,共8页
Journal of South China University of Technology(Natural Science Edition)
基金
国家自然科学基金资助项目(62071411)。
