新的具有宽参数范围的五维保守超混沌系统的动力学研究  

Dynamic study of a new five-dimensional conservative hyperchaotic system with wide parameter range

作　　者：张泽峰 黄丽莲[1,2] 项建弘 刘帅[1,2] Zhang Ze-Feng;Huang Li-Lian;Xiang Jian-Hong;Liu Shuai(College of Information and Communication Engineering,Harbin Engineering University,Harbin 150001,China;MIIT Key Laboratory of Advanced Marine Communication and Information Technology,Harbin Engineering University,Harbin 150001,China)

机构地区：[1]哈尔滨工程大学信息与通信工程学院,哈尔滨150001 [2]哈尔滨工程大学,先进船舶通信与信息技术工业和信息化部重点实验室,哈尔滨150001

出　　处：《物理学报》2021年第23期122-132,共11页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:61203004);黑龙江省自然科学基金(批准号:F201220);黑龙江省自然科学基金联合引导项目(批准号:LH2020 F022)资助的课题.

摘　　要：保守系统因为没有吸引子,与常见的耗散系统相比,它的遍历性更好,伪随机性更强,安全性更高,更适合应用于混沌保密通信等领域.基于此,设计了一个新的具有宽参数范围的五维保守超混沌系统.首先,进行Hamilton能量和Casimir能量分析,证明了新系统满足Hamilton能量保守且能够产生混沌.然后进行动力学分析,包括保守性证明、平衡点分析、Lyapunov指数谱和分岔图分析,证明了新系统具有保守系统的特点,且能够在宽参数范围内一直保持超混沌状态,同时对比宽参数范围内系统的相图和Poincaré截面图,结果表明随着参数增大,系统的随机性和遍历性得到增强.接着,对新系统进行NIST测试,结果显示该系统在宽参数范围内产生的混沌随机序列具有很强的伪随机性.最后对保守超混沌系统进行电路仿真和硬件电路实验,实验结果证实了新系统具有良好的遍历性和可实现性.Conservative systems have no attractors.Therefore,compared with common dissipative systems,conservative systems have good ergodicity,strong pseudo-randomness and high security performance,thereby making them more suitable for applications in chaotic secure communication and other fields.Owing to these features,a new five-dimensional conservative hyperchaotic system with a wide parameter range is designed.Firstly,the Hamiltonian energy and Casimir energy are analyzed,showing that the new system satisfies the Hamiltonian energy conservation and can generate chaos.Next,the dynamic analysis is carried out,including conservativeness proof,equilibrium point analysis,Lyapunov exponential spectrum,and bifurcation diagrams analysis,thereby proving that the new system has the characteristics of conservative system and can always maintain a hyperchaotic state in a wide parameter range.At the same time,the phase diagram and Poincarésection diagram of the new system in a wide parameter range are compared.The results show that the randomness and ergodicity of the system are enhanced with the increase of parameters.Then,the NIST test shows that the chaotic random sequences generated by the new system in a wide parameter range have strong pseudo-randomness.Finally,the circuit simulation and hardware circuit experiment of the conservative hyperchaotic system are carried out,which proves that the new system has good ergodicity and realizability.

关 键 词：宽参数范围 保守超混沌系统 随机性 遍历性 

分 类 号：O415.5[理学—理论物理]