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Local and global stability analysis methods of multitime scale neural networks

The dynamics of complex neural networks modeling the self-organization process in cortical maps must include the aspects of long and short-term memory. The behavior 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 as a global analysis technique and the theory of singular perturbations as a local analysis method. We also show the consequences of the stability analysis on the neural net parameters.