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30 April 2007 Global stability analysis of competitive neural networks under perturbations
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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.
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Anke Meyer-Baese and Helge Ritter "Global stability analysis of competitive neural networks under perturbations", Proc. SPIE 6560, Intelligent Computing: Theory and Applications V, 65600F (30 April 2007);

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