On matrices with common invariant cones with applications in neural and gene networks

被引：11

作者：

Edwards, R

McDonald, JJ

Tsatsorneros, MJ

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3P4, Canada

[2] Washington State Univ, Dept Math, Pullman, WA 99164 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2005年 / 398卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

invariant coned proper cone; invariant subspace; matrix word; nonnegative matrix; Perron-Frobenius; tensor product; compound matrix; exterior product; decomposable vector; dominant eigen-vector; Glass network; gene network; neural network; cantor set;

D O I：

10.1016/j.laa.2004.04.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Motivated by a differential continuous-time switching model for gene and neural networks, we investigate matrix theoretic problems regarding the relative location and topology of the dominant eigenvectors of words constructed multiplicatively from two matrices A and B. These problems are naturally associated with the existence of common invariant subspaces and common invariant proper cones of A and B. The commuting case and the two-dimensional case are rich and considered analytically. We also analyze and recast the problem of the existence of a common invariant polyhedral cone in a multilinear framework, as well as present necessary conditions for the existence of low dimensional common invariant cones. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：37 / 67

页数：31

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