一类梯形激活函数的细胞神经网络的静态解及Smale马蹄  

The stationary solutions of a class of cellular neural networks with trapezoidal activation function and Smale horseshoe

作　　者：陈芳跃[1] 汤文辉[1] 

机构地区：[1]浙江师范大学数理与信息工程学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2008年第1期8-16,共9页Journal of Zhejiang Normal University:Natural Sciences

摘　　要：研究了一类以梯形激活函数为输出函数的细胞神经网络.通过将a-z平面分解成25个不交的区域,分析了这类细胞神经网络的静态解.其中,a和z(即反馈系数和阈值)被视为参数.当给定参数时,每个区间内该类细胞神经网络的静态解的范围被确定.针对一类特殊的梯形激活函数的细胞神经网络,研究了其静态解诱导的映射产生的Sm ale马蹄的充分条件,说明了该映射的复杂性.A class of cellular neural network （CNN） with trapezoidal activation function（CNNwTAF） was discussed. With the a - z plane been partitioned into 25 disjoint open regions, where parameters a and z stand for the output synaptic weight and system threshold respectively, the stationary solutions of CNNwTAFs were discussed and some useful results were obtained. Moreover, for a special kind of CNNwTAF, the sufficient conditions of the existence of Smale horseshoe induced by the stationary solutions＇ maps were studied, which in part implied the complexity of the maps.

关 键 词：细胞神经网络 梯形激活函数 参数空间 静态解 SMALE马蹄 

分 类 号：O175[理学—数学]