Diamond in multi-layer cellular neural networks

This investigation considers the complexity of output spaces of multi-layer cellular neural networks. Let B be a set of admissible local output patterns coupled with input and let B∼ be the set of admissible output patterns extracting from B. Since topological entropy is an indicator for investigating the complexity of spaces, we study the topological entropy of output spaces YU and Y which are induced by B and B∼, respectively. A system has a diamond if h(YU)≠h(Y). Necessary and sufficient conditions for the existence of diamond are demonstrated separately. Furthermore, numerical experiments exhibit some novel phenomena.