IEEE Trans. Circuits Syst. I, 4(47), p. 568-571
DOI: 10.1109/81.841858
World Scientific Publishing, International Journal of Neural Systems, 01(13), p. 47-53
DOI: 10.1142/s012906570300139x
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The dynamics of cortical cognitive maps developed by self–organization 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 biologically relevant system. We present new stability conditions for analyzing the dynamics of a biological relevant system with different time scales based on the theory of flow invariance. We prove the existence and uniqueness of the equilibrium, and give a quadratic–type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables and thus prove the global stability of the equilibrium point.