一类混合延迟混沌神经网络的同步

Synchronization of a Class of Chaotic Neural Networks with Mixed Time Delays

时滞混沌神经网络系统是解空间为无穷维系统,可生成多个正向Lyapunov指数,产生具有高度随机性和不可预测性的混沌甚至超混沌序列,这种特性使得时滞混沌神经网络系统特别适用于保密通信中,混沌同步是保密通信中的关键技术。基于Lyapunov稳定性理论和线性矩阵不等式(LMI)方法,研究了一类具有时变延迟和分布式延迟的混沌神经网络系统的同步问题,考虑系统的内部参数不确定性和外部干扰及混合时滞等因素,将系统时滞项加入所设计的控制器中,给出了保证误差系统的全局均方渐近稳定的充分条件和控制律,实现驱动系统和响应系统的同步。与其它方法相比,所设计的含有时滞项的控制器提高了系统误差精度及反应速率。最后,通过仿真实例,验证了所提方法的有效性。

The solution space of delay chaotic neural network system is infinite - dimensional, which can generate a large numbers of positive Lyapunov exponents, as well as chaotic or even hyper - chaotic time series with highly randomness and unpredictability. This character makes the system especially suitable for secured communication of which chaotic synchronization is a key technology. In this paper, a synchronization control for a class of chaotic neural networks combining time - varying delay and distributed delay is investiga- ted based on Lyapunov Stability Theory and Linear Matrix Inequality （LMI） method. By considering factors such as internal parameter uncertainty, external stochastic perturbation and mixed delay, the system time delay is added to designed controller. Then the sufficient condition and control law are obtained, which guarantee global asymptotic stability of the error system. At the mean time, the synchroni- zation between the response and driven systems is achieved. Compared with other methods, the proposed method in this paper can im- prove the accuracy of the system error and response rates. Finally, a numerical example is also given to verify its effectiveness.