Quadratic-type Lyapunov functions for competitive neural networks with different time-scales

The dynamics of complex neural networks must include the aspects of long and short-term memory. The behaviour of the network is characterized by an equation of neural activity as a fast phenomenon and by an equation of synaptic modification as a slow part of the neural system. We present a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables.