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.
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