Global exponential stability of competitive neural networks with different time scales

• Published in: IEEE transaction on neural networks and learning systems 2003-05, Vol.14 (3), p.716-719
• Main Authors: Meyer-Baese, A., Pilyugin, S.S., Chen, Y.
• Format: Article
• Language: English
• Subjects: Backpropagation algorithms; Biological neural networks; Cognition & reasoning; Equations; Lyapunov method; Multi-layer neural network; Neural networks; Neurons; Recurrent neural networks; Robust stability; Supervised learning
• ISSN: 1045-9227; 2162-237X; 1941-0093; 2162-2388
• DOI: 10.1109/TNN.2003.810594

The dynamics of cortical cognitive maps developed by self-organization must include the aspects of long and short-term memory. The behavior of such a neural network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system. We present a new method of analyzing the dynamics of a biological relevant system 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.