Author:
Ivanov Sergey,Kipnis Mikhail,Medina Rigoberto
Abstract
Abstract
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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference19 articles.
1. Vishwanathan A, Bi GQ, Zeringue HC: Ring-shaped neuronal networks: a platform to study persistent activity. Lab Chip 2011, 11(6):1081–1088. 10.1039/c0lc00450b
2. Kaslik E: Dynamics of a discrete-time bidirectional ring of neurons with delay. In Proceedings of Int. Joint Conf. on Neural Networks. IEEE Comput. Soc., Los Alamitos; 2009:1539–1546. Atlanta, Georgia, USA, 14–19 June 2009
3. Kaslik E, Balint S: Complex and chaotic dynamics in a discrete-time delayed Hopfield neural network with ring architecture. Neural Netw. 2009, 22(10):1411–1418. 10.1016/j.neunet.2009.03.009
4. Yuan Y, Campbell SA: Stability and synchronization of a ring of identical cells with delayed coupling. J. Dyn. Differ. Equ. 2004, 16: 709–744. 10.1007/s10884-004-6114-y
5. Khokhlova TN, Kipnis MM: The breaking of a delayed ring neural network contributes to stability: the rule and exceptions. Neural Netw. 2013, 48: 148–152.