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MiS Preprint
53/2007

Almost periodic dynamics of a class of delayed neural networks with discontinuous activations

Wenlian Lu and Tianping Chen

Abstract

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.

Received:
04.06.2007
Published:
04.06.2007
MSC Codes:
34K14, 34D23, 45J05
PACS:
02.30.Ks, 84.35.+i
Keywords:
Delayed integro-differential system, discontinuous activation, almost periodic function, global exponential stability

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inJournal
2008 Repository Open Access
Wenlian Lu

Almost periodic dynamics of a class of delayed neural networks with discontinuous activations

In: Neural computation, 20 (2008) 4, pp. 1065-1090