Asymptotic behavior of a BAM neural network with delays of distributed type

In this paper, we examine a Bidirectional Associative Memory neural network model with distributed delays. Using a result due to Cid [J. Math. Anal. Appl. 281 (2003) 264-275], we were able to prove an exponential stability result in the case when the standard Lipschitz continuity condition is violated. Indeed, we deal with activation functions which may not be Lipschitz continuous. Therefore, the standard Halanay inequality is not applicable. We will use a nonlinear version of this inequality. At the end, the obtained differential inequality which should imply the exponential stability appears 'state dependent'. That is the usual constant depends in this case on the state itself. This adds some difficulties which we overcome by a suitable argument.

Automated summary

This paper examines a neural network model with distributed delays and proves an exponential stability result when the standard Lipschitz continuity condition is violated. The study deals with activation functions that may not be Lipschitz continuous, and a nonlinear version of the Halanay inequality is used to overcome difficulties. The obtained differential inequality for exponential stability is 'state dependent,' with the usual constant depending on the state itself.