## On the Structure of Multilayer Cellular Neural Networks: Complexity between Two Layers

**Jung-Chao Ban***

*Department of Applied Mathematics, National Dong Hwa University**Hualian 97401, Taiwan, ROC*

**Chih-Hung Chang ^{†}**

*Department of Applied Mathematics, National University of Kaohsiung**Kaohsiung 81148, Taiwan, ROC *jcban@mail.ndhu.edu.tw^{†}Corresponding author: chchang@nuk.edu.tw*

#### Abstract

Let be the solution space of an *n*-layer cellular neural network, and let and be the hidden spaces, where , . ( is called the output space.) The classification and the existence of factor maps between two hidden spaces that reach the same topological entropies are investigated in [1]. This paper elucidates the existence of factor maps between those hidden spaces carrying distinct topological entropies. For either case, the Hausdorff dimensions and can be calculated. Furthermore, the dimensions of and ) are related by the factor map between them.