Almost periodic dynamics of a class of delayed neural networks with discontinuous activations
Wenlian Lu and Tianping Chen
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Submission date: 04. Jun. 2007
published in: Neural computation, 20 (2008) 4, p. 1065-1090
DOI number (of the published article): 10.1162/neco.2008.10-06-364
MSC-Numbers: 34K14, 34D23, 45J05
PACS-Numbers: 02.30.Ks, 84.35.+i
Keywords and phrases: Delayed integro-differential system, discontinuous activation, almost periodic function, global exponential stability
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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, interconnections 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. Furthermore, 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 actually approximates to the Filippov solution of the dynamical system with discontinuous activations.