CNN超混沌系统的多元同步及其应用研究

Diversification Synchronization for Hyper Chaos of Cellular Neural Network and its Application Research

基于同步误差系统的线性稳定性准则,将细胞神经网络驱动系统适当的拆分为线性和非线性两个部分,在满足雅可比矩阵的特征值全为负的情况下,构造出新的动力学系统作为响应系统.由于满足同步条件的雅可比矩阵具有多值性,最终能够得到与同一驱动系统对应的响应系统不是唯一的,因此可以构造多元的响应系统.通过比较不同雅克比矩阵的特征值与初始值的变化,验证系统误差变化规律,数值仿真结果表明该同步方法的多元化和有效性.并将该同步方法应用于信号隐匿、文本置乱与图像加密中,仿真结果表明了该同步方法具有现实可行性.

CNN drive system is properly divided into linear and nonlinear based on the linear stability criterion of synchronous error system, and then a new dynamics system is constructed to be a response system in the case that all the eigenvalues of Jacobian matrix are negative. Due to the multiple values of eigenvalues of Jacobian matrix meeting the synchronization conditions, the response system corresponding to the same drive system is not only, therefore, we can construct a new dynamic system as diverse response system. The variation regularity for system error is verified by comparing the changes of different eigenvalues of Jacobian matrix and initial value, and the results of numerical simulation show that the synchronization method is diverse and effective. And the applications of signal hiding, text scrambling and image encryption prove that the synchronization method has feasibility.