一个新的具有超级多稳态的五维忆阻超混沌系统

A novel five-dimensional memristive hyperchaotic system with extreme multistability

为了描述更加复杂的非线性动力学特性并且得到更适合工程应用的混沌信号,使用一个磁控忆阻器去替换改进的四维Lü混沌系统中的耦合参数,得到了一个新的五维忆阻超混沌系统。采用相图、分岔图、Lyapunov指数谱等常规的非线性分析手段研究新系统丰富的动力学特性。在新系统的基础上,通过引入一个绝对值函数使系统达到新的极性平衡,构建了一个新的条件对称的忆阻超混沌系统。结果表明:新的忆阻系统可以表现出依赖于忆阻器初始状态的超级多稳态特性、持续的混沌或超混沌动力学以及偏移增量控制行为;特别地,当改变系统参数并取适当的初始状态时,可以观察到独特的共存超级多稳态现象;新的条件对称忆阻系统可产生无限多对具有相反极性且吸引子结构相似的共存吸引子。利用Multisim进行电路仿真,验证了系统的存在性和可实现性,从而使超混沌系统能更好地应用在保密通信等实际工程领域。

In order to describe more complex nonlinear dynamic characteristics and obtain chaotic signals that are more suitable for engineering applications, a flux-controlled memristor was used to replace the coupling parameter in the improved four-dimensional Lü chaotic system, and a new five-dimensional memristive hyperchaotic system was proposed. The rich dynamic characteristics of the new system were studied by using conventional nonlinear analysis methods such as phase diagram, bifurcation diagram, and Lyapunov exponential spectrum. On the basis of the new system, by introducing an absolute value function into the system to make it reach a new polarity balance, a new conditionally symmetric memristive hyperchaotic system was constructed. Results show that the new memristive system could exhibit extreme multistability phenomena dependent on the initial states of the memristor, sustained chaotic or hyperchaotic dynamics, and offset-boosting control behaviors. In particular, when changing the system parameters and taking appropriate initial states, a unique coexisting extreme multistability phenomenon was observed. The conditionally symmetric memristive system could generate an infinite number of pairs of coexisting attractors with opposite polarities and similar attractor sizes. The existence and achievability of the new system was verified through circuit simulation using Multisim, so that the hyperchaotic system can be better applied in practical engineering fields such as secure communications.