【摘要】 分别设计了忆阻器、忆感器、忆容器的通用数学模型,并以此为基础构造了简单的并联混沌系统,分析了包括相图、时域图、Lyapunov指数、功率谱、庞加莱截面在内的动力学特性,证明了其超混沌特性。进一步研究了平衡点稳定性、系统参数及初始值对系统的影响,研究结果表明:参数的对称性变化会引起系统状态相应的对称性变化;而在系统能混沌振荡的情况下,初始值不影响系统的状态。最后利用Multisim进行了电路仿真,数值仿真与实验结果呈现出较好的一致性,证明该系统的现实可行性与实际存在性。该系统的研究既扩展了记忆元件在非线性范畴的应用,又为基于记忆元件的超混沌系统的实际应用奠定了基础。更多还原

【Abstract】 The universal mathematical models of memristor, meminductor and memcapacitor are designed respectively, and based on these models, a simple parallel chaotic system is constructed. The dynamic characteristics of the system including phase diagram, time domain diagram, Lyapunov index,power spectrum and poincare cross section are analyzed, and its hyperchaotic characteristics are proved.The influence of equilibrium point stability, system parameters and initial value on the system is further studied. And it is shown that the symmetry change of parameters will cause the corresponding symmetry change of system state, however, the initial value does not affect the state of the system under the condition of chaotic oscillation. Finally, the circuit is designed and realized by using Multisim, and the numerical simulation results are in good agreement with the experimental results, which proves the practical feasibility and actual existence of the system. This work not only extends the application of memory element in the nonlinear category, but also makes the basic work for the practical application of memory element based hyperchaotic system.更多还原