Global stability analysis of competitive neural networks under perturbations
Anke Meyer‐Baese, Helge Joachim Ritter · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2007
We establish stability results for both competitive neural networks with only neural activity levels and also with different time-scales under parameter perturbations and determine conditions that ensure the existence of exponentially stable equilibria of the perturbed neural system. The perturbed neural system is modeled as nonlinear perturbations to a known nonlinear idealized system and is represented by both a short-term memory subsystem and also by a two time-scale subsystem. Based on the theory of sliding mode control, we can determine for the simple competitive model a reduced-order system and show that if it is asymptotically stable then the full system will also be asymptotically stable. In addition, a region of attraction can be found. For the two time-scales neural systems, we derive a Lyapunov function for the coupled system and a maximal upper bound for the fast time scale associated with the neural activity state.