Local and Global Stability Analysis Methods of Multi-Time Scale Neural Networks

摘要

The dynamics of complex neural networks modelling the self-organization process in cortical maps must include the aspects of long and short-term memory. The behaviour of the network is such 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 new methods of analyzing the dynamics of a competitive neural system with different time scales: The K-monotone system theory developed by Kamke in 1932{sup}Hir85 as a global analysis techniques and the theory of singular perturbations{sup}Vid93 as a local analysis method. We also show the consequences of the stability analysis on the neural net parameters.