Title :
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
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;
Conference_Titel :
Neural Networks, 2004. Proceedings. 2004 IEEE International Joint Conference on
Print_ISBN :
0-7803-8359-1
DOI :
10.1109/IJCNN.2004.1380176
