具有多稳态和可调数目吸引子共存的混沌系统

兰州理工大学学报 ›› 2022, Vol. 48 ›› Issue (6): 88-95.

• 自动化技术与计算机技术 • 上一篇下一篇

具有多稳态和可调数目吸引子共存的混沌系统

颜闽秀^*1,2, 谢俊红¹, 张帅³

1.沈阳化工大学信息工程学院, 辽宁沈阳 110142;
2.工业环境-资源协同控制与优化技术辽宁省高校重点实验室, 辽宁沈阳 110142;
3.东北大学信息科学与工程学院, 辽宁沈阳 110004

收稿日期:2021-05-18 出版日期:2022-12-28 发布日期:2023-03-21
通讯作者: 颜闽秀(1972-),女,福建仙游人,博士,副教授.Email:yanminxiu@syuct.edu.cn
基金资助:
中国-北马其顿政府间科技合作项目(国科外[2019]22:6-8)

Chaotic system with multistable and adjustable number of attractors

YAN Min-xiu^1,2, XIE Jun-hong¹, ZHANG Shuai³

1. College of Information Engineering, Shenyang University of Chemical Technology, Shenyang 110142, China;
2. Key Laboratory for Industrial Environment-Resources Cooperative Control and Optimization Technology (University of Liaoning Province), Shenyang 110142, China;
3. College of Information Science and Engineering, Northeast University,Shenyang 110004, China

Received:2021-05-18 Online:2022-12-28 Published:2023-03-21

摘要/Abstract

摘要： 由于在混沌系统中,具有多稳态性和可调数目的混沌吸引子在安全通信中有着重要的研究潜力,因此试图建立一个具有多稳态性和可调数目的混沌系统是有意义的.针对此问题,在传统耗散混沌系统的基础上,建立了一个模型较为简单的混沌系统,通过分析系统的动力学特性,验证了随着初始条件的不同,系统在同一相空间中能够产生不同的吸引子共存,进而验证了该系统的多稳态性.在其基础上,将双曲正切函数引入该系统,通过扩展系统平衡点的方法产生吸引子共存,建立了具有可调数目的吸引子的共存,并通过相关理论研究和数值模拟仿真对其进行了验证.最后,基于模型系统进行了模拟电路的实验和验证,表明了该系统能够实现的可能性.

关键词: 耗散混沌系统, 双曲正切函数, 多稳态性, 吸引子的共存, 电路实现

Abstract: In chaotic system, chaotic attractors with multistability and adjustable number have important research potential in secure communication. Therefore, it is meaningful to try to build a chaotic system with multistability and adjustable number. Based on the traditional dissipative chaotic system, a simple model of chaotic system is established. By analyzing the dynamic characteristics of the system, it is verified that different attractors can coexist in the same phase space with different initial conditions, and then the multistability of the system is verified. On this basis, the hyperbolic tangent function is introduced into the system. The coexistence of attractors is generated by expanding the equilibrium point of the system, and the coexistence of attractors with adjustable number is established which is verified by relevant theoretical research and numerical simulation. Finally, the experiments and validation of the simulated circuit based on the model system were carried out, which indicate the possibility of the system implementation. Due to the complexity of the dynamic behavior of the coexistence of multisteady state and attractor, the system has good application potential in the field of secure communication.

Key words: dissipate chaotic system, hyperbolic tangent function, multistability, coexistence of attractors, circuit implementation

中图分类号:

TP11
O415.5

颜闽秀, 谢俊红, 张帅. 具有多稳态和可调数目吸引子共存的混沌系统[J]. 兰州理工大学学报, 2022, 48(6): 88-95.

YAN Min-xiu, XIE Jun-hong, ZHANG Shuai. Chaotic system with multistable and adjustable number of attractors[J]. Journal of Lanzhou University of Technology, 2022, 48(6): 88-95.

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具有多稳态和可调数目吸引子共存的混沌系统

Chaotic system with multistable and adjustable number of attractors

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