高维混沌系统的多元函数投影同步及其保密通信方案

Multivariable Function Projective Synchronization of High Dimensional Chaotic Systems and Its Secure Communication Scheme

提出一种改进的函数投影同步方案——多元函数投影同步。与现有的比例因子为一元函数的函数投影同步方案不同,本文讨论的比例因子为多元函数。在该方案下,系统间的同步行为更复杂、更难以预测,驱动与响应系统将在更高的维度中展现出相关性。基于改进的主动控制方法,研究四维能源系统和超混沌蔡氏系统的多元函数投影同步问题,并设计同步控制器。在数值模拟中,分别针对比例因子为多元线性函数和多元非线性函数情况进行同步仿真,实现了系统之间的多元函数投影同步。利用上述同步,设计相应的保密通信方案,以正弦信号和灰度图像信号作为信息信号进行保密通信仿真,并通过引入小波阈值去噪算法进行抗噪声模拟。结果表明:提出的同步方案可行,所设计的保密通信方法有效,具备较好的保密性和稳健性。

A modified function projective synchronization scheme,multivariable function projective synchronization,is proposed.Different from existing function projective synchronization schemes whose scaling factor is unary function,the scaling factor discussed in this scheme is multivariable function.It implies that synchronization behavior of the proposed scheme is more complicated and more unpredictable.The driver and responding system show correlation in a higher dimension.With modified active control method,controller of the synchronization is designed.In numerical simulations,four-dimensional energy resources system and a new hyperchaotic Chua system are investigated.Multivariable function projective synchronization with two types of scaling factor between two systems are achieved.Based on the synchronization,a secure communication scheme is designed.A secure communication simulation is carried out with sinusoidal signal and gray image signal as information signals.Meanwhile,anti-noise simulation is performed with a wavelet threshold denoising algorithm.It shows that the synchronization method is feasible,and the secure communication scheme is effective.