中文摘要：

忆阻器是一种具有记忆功能和纳米级尺寸的非线性元件,作为混沌系统的非线性部分,能够使系统的物理尺寸大大减小,同时可以得到各种丰富的非线性曲线,提高混沌系统的复杂度和信号的随机性.因此,本文采用离子迁移忆阻器的磁控模型设计了一个新的混沌系统.通过理论推导、数值仿真、Lyapunov指数谱、分岔图和Poincaré截面图研究了系统的基本动力学特性,并分析了改变不同参数时系统动力学行为的变化.同时,建立了模拟该系统的SPICE电路,SPICE仿真结果与数值分析相符,从而验证该混沌系统的混沌产生能力.最后,利用线性反馈同步控制方法实现了新构造的离子迁移忆阻混沌系统的同步,并且采用该同步方法有效实现了语音信号的保密通信.数值仿真证实了新混沌系统的存在性以及同步控制应用的可行性.

英文摘要：

A memristor is a nonlinear element of nanoscale size with memory function and when it works as the nonlinear part in a chaotic system, the physical size of the system will be greatly reduced, rich nonlinear curve will be produced, and at the same time, the complexity of the chaotic systems and the randomness of signals will be enhanced. So in this paper, a new chaotic system is designed based on an ion migration memristor. The complex dynamic characteristics of the memristive system are investigated by means of theoretical derivation, numerical simulation, Lyapunov exponent spectrum, power spectrum, and Poincaré map. In addition, the change of system dynamic behaviors with the different parameters are analyzed. Then, a SPICE-based analog circuit is presented. The SPICE simulation results are in conformity with the numerical analysis, and thus verify that the chaotic systems can produce chaos. The linear feedback control structure is simple, economic and easy to realize in engineering practice, so the linear feedback control method has a high application value. At present, most studies focus on memristors＇ applications in memory and analog neural networks, but little research work is for voice security transmission. Therefore, by using the method of linear feedback control of chaotic synchronization, this paper proves the effectiveness of this method by numerical simulation experiments. As a result,it can achieve secure communication of voice signals. Finally, we conclude that the linear synchronous control method based on memristive chaotic system when applied to the secure communications can achieve the purpose of covering a specific speech. In addition, this method is able to restore the specific speech signal without distortion, which is very meaningful for the promotion of applications of memristor.