| 一类梯形激活函数的细胞神经网络的静态解及Smale马蹄 |
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| 引用本文： | 陈芳跃,文辉. 一类梯形激活函数的细胞神经网络的静态解及Smale马蹄[J]. 浙江师范大学学报(自然科学版), 2008, 31(1): 8-16 |
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| 作者姓名： | 陈芳跃 文辉 |
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| 作者单位： | 浙江师范大学,数理与信息工程学院,浙江,金华,321004 |
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| 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Smale马蹄的充分条件，说明了该映射的复杂性．
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| 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 |
| 文章编号： | 1001-5051（2008）01-0008-09 |
| 收稿时间： | 2007-11-12 |
| 修稿时间： | 2007-11-28 |
The stationary solutions of a class of cellular neural networks with trapezoidal activation function and Smale horseshoe |
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| CHEN Fangyue,TANG Wenhui. The stationary solutions of a class of cellular neural networks with trapezoidal activation function and Smale horseshoe[J]. Journal of Zhejiang Normal University Natural Sciences, 2008, 31(1): 8-16 |
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| Authors: | CHEN Fangyue TANG Wenhui |
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| Affiliation: | ( College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua Zhejiang 321004, China ) |
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| Abstract: | 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. |
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| Keywords: | cellular neural network trapezoidal activation function（TAF） parameters space stationary solutions Smale horseshoe |
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