On the stability of the Cartesian product of a neural ring and an arbitrary neural network

Advances in Difference Equations

Rigoberto Medina¹  Mikhail Kipnis²  Sergey Ivanov² 

[1] Departamento de Ciencias Exactas, Universidad de Los Lagos, Casilla, Osorno, Chile;Department of Mathematics, Chelyabinsk State Pedagogical University, Chelyabinsk, Russia

关键词: stability;    discrete-time model;    ring of neural networks;    Cartesian product of networks;    the stability cone;   

DOI  :  10.1186/1687-1847-2014-176

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The stability of a system of neural networks connected to a ring has been studied extensively throughout recent years. Our main contribution within this work states that the stability region in the parameter space of a discrete-time model can be extended by breaking such a ring provided that there is a sufficiently large number of networks. Also, it has been shown that for a small ring, paradoxical values may appear within its parameter space for which such a ring is stable; meanwhile, corresponding linear configuration is unstable. MSC:37B25.

【 授权许可】

CC BY