具有逐段常变量神经网络系统的伪概周期解

Pseudo Almost Periodic Solutions for the Cellular Neural Networks with Piecewise Constant Argument

结合生物模型,针对一类具有逐段常变量神经网络系统的伪概周期解的存在性问题,利用伪概周期函数的等价定义、相关性质以及相应的差分方程进行了研究.依据逐段常变量微分方程的解在一点的连续性,构造了一个差分方程,利用差分方程的伪概周期序列解以及方程中有关函数给出了这类微分方程的伪概周期解存在的充分条件.此类神经网络系统结合了微分方程和差分方程的性质,可应用到模式识别、信号处理、联想记忆等方面.

Combining with biomedical models,the existence of pseudo almost periodic solution is studied for the cellular neural networks with piecewise constant argument by the definition of pseudo almost periodic function,relevant properties and difference equations.By the continuity of the solution,building a different equation,the sufficient conditions of the existence of pseudo almost periodic solution are given basing on pseudo almost periodic sequence solution of a difference equation and other functions of the equation.The cellular neural networks combines the properties of differential equations and difference equations,and it can be applied in mode recognition,signal processing and imagining memory and so on.