Stability analysis of a self-organizing neural network with feedforward and feedback dynamics

Author

Meyer-Base, A. ; Pilyugin, Sergei S. ; Wismuller, Axel

Author_Institution

Dept. of Electr. & Comput. Eng., Florida State Univ., Tallahassee, FL, USA

Volume

2

fYear

2004

fDate

25-29 July 2004

Firstpage

1505

Abstract

We present a new method of analyzing the dynamics of self-organizing neural networks with different time scales based on the theory of flow invariance. We are able to show the conditions under which the solutions of such a system are bounded being less restrictive than with the K-monotone theory, singular perturbation theory, or those based on supervised synaptic learning. We prove the existence and the uniqueness of the equilibrium. A strict Lyapunov function for the flow of a competitive neural system with different time scales is given, and based on it we are able to prove the global exponential stability of the equilibrium point.

Keywords

Lyapunov methods; asymptotic stability; differential equations; feedback; feedforward neural nets; learning (artificial intelligence); self-organising feature maps; K-monotone theory; Lyapunov function; competitive neural system; differential equations; feedback dynamics; feedforward neural network; flow invariance theory; global exponential stability; self organizing neural network; singular perturbation theory; stability analysis; supervised synaptic learning; Backpropagation algorithms; Biological neural networks; Equations; Feedforward neural networks; Neural networks; Neurofeedback; Neurons; Organizing; Stability analysis; Supervised learning;

fLanguage

English

Publisher

ieee

Conference_Titel

Neural Networks, 2004. Proceedings. 2004 IEEE International Joint Conference on

ISSN

1098-7576

Print_ISBN

0-7803-8359-1

Type

conf

DOI

10.1109/IJCNN.2004.1380176

Filename

1380176