On matrices with common invariant cones with applications in neural and gene networks
The authors describe and investigate matrix theoretic problems that arise in the study of the dynamic of Glass networks. Glass networks are described in detail in Section 2. Sections 3 and 4 contain notation, definition and preliminary observations regarding invariant set and cones. In Section 5 they consider the topological properties of the set of all words of finite length constructed from two matrices. In Section 6, they consider the case of commuting matrices. The problem of common invariant proper cones is examined for \(2\times 2\) matrices in Section 7. The case of common invariant polyhedral cones is analyzed and recast in a multilinear framework in Section 8.
scientific article; zbMATH DE number 2165372
scientific article