Local uniform stability of competitive neural networks with different time-scales under vanishing perturbations

We prove local uniform stability for a class of parametric uncertain competitive multi-time scale neural networks and determine the conditions under which stability holds as simple relationships between the neural parameters. It is assumed that the resulting parametric perturbations are only limited by their bounds. The stability conditions are established based on Gershgorin's Theorem and at the same time a more realistic upper bound is obtained than with the conservative method for the fast time scale associated with the neural activity state.