Robust stability analysis of Linsker-Type Hebbian learning multi-time scale neural networks under parametric uncertainties

A novel network based on Linsker-type Hebbian learning is analyzed in its dynamical behavior. The network combines a coupled dynamics of fast and slow states and is prone to internal parametrical fluctuations as well as external noises. Robustness represents a crucial property of the network to attenuate the effects of internal fluctuation and external noise. In this study, we formulate this novel neural network as a coupled nonlinear differential systems operating at different time-scales under vanishing perturbations. We determine conditions for the existence of a global uniform attractor of the perturbed biological system. By using a Lyapunov function for the coupled system, we derive a maximal upper bound for the fast time scale associated with the fast state. Finally, two examples are given to confirm the applicability of the developed theoretical framework.