Abstract: In terms of an analysis of the nonlinear, asymmetric dynamics of Linsker's layered self-adaptive network, we first determine the whole set of fixed point attractors of the network and their stability is established. A necessary and sufficient condition for the emergence of a structured receptive field is presented. Thus the parameter regime to ensure the development of a desired structured receptive field can be obtained explicitly. For given synaptic density functions, the parameter regime of (k₁，k₂), in which a structured pattern of connection strengths develops, is a band between two parallel lines. The breadth of the band is given by d₁(·) and d₂(·) depending on the covariance matrix q. The shape of the receptive field is totally governed by the synaptic density function between source and target cell layers and so by k₁, k₂, while the existence of a parameter regime for the occurrence of such a receptive field is determined by d₁(·), d₂(·), and therefore by the covariance matrix q. According to results above, we then refigure the emergence of various structured connection strengths between the second and third layer in detail. In principle, our rigorous analysis based upon the nonlinear dynamics of Linsker's network conforms with most of results gained in the numerical simulation and linear analysis of Linsker's network before. Of course, a modification of some of them is carried out here.

Key words: Synaptic density function, attractor, on-center Cell, receptive field

摘要： 给出了Linsker网络出现有结构感受野的充要条件，对于给定的Synaptic密度函数，参数(k₁，k₂)能产生感受野的区域介于两条平行直线之间，这两条平行直线之间的距离d₂～d₁由协方差矩阵q所决定。作为上述一般性结果的一个应用，对于Ｂ－Ｃ层的Linsker网络进行了具体分析。

关键词: Linsker网络, 吸引子, 感受野, Synaptic密度函数