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Almost periodic dynamics of a class of delayed neural networks with discontinuous activations. (English) Zbl 1146.68422

Neural Comput. 20, No. 4, 1065-1090 (2008); erratum ibid. 25, No. 12, 3340-3342 (2013).
Summary: We use the concept of the Filippov solution to study the dynamics of a class of delayed dynamical systems with discontinuous right-hand side, which contains the widely studied delayed neural network models with almost periodic self-inhibitions, interconnection weights, and external inputs. We prove that diagonal-dominant conditions can guarantee the existence and uniqueness of an almost periodic solution, as well as its global exponential stability. As special cases, we derive a series of results on the dynamics of delayed dynamical systems with discontinuous activations and periodic coefficients or constant coefficients, respectively. From the proof of the existence and uniqueness of the solution, we prove that the solution of a delayed dynamical system with high-slope activations approximates to the Filippov solution of the dynamical system with discontinuous activations.

MSC:

68T05 Learning and adaptive systems in artificial intelligence
34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
37N25 Dynamical systems in biology
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