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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
61/2007

$R^{n}_{+}$-global stability of Cohen-Grossberg neural network system with nonnegative equilibria

Wenlian Lu and Tianping Chen

Abstract

In this paper, without assuming strict positivity of amplifier functions, boundedness of activation functions, or symmetry of connection matrix, the dynamical behaviors of delayed Cohen-Grossberg neural networks with nonnegative equilibrium are studied. Based on the theory of nonlinear complementary problem (NCP), a sufficient condition is derived guaranteeing existence and uniqueness of the nonnegative equilibrium in the NCP sense. Moreover, this condition also guarantees the $R^{n}_{+}$-global asymptotic stability of the nonnegative equilibrium in the first orthant. The result is compared with some previous results and a numerical example is presented to indicate the viability of our theoretical results.

Received:
Jun 30, 2007
Published:
Jun 30, 2007
MSC Codes:
34D23, 34K20
Keywords:
Cohen Grossberg neural networks, nonnegative equilibrium, $R^{n}_{+}$ global stability

Related publications

inJournal
2007 Repository Open Access
Wenlian Lu and Tianping Chen

Rn+-global stability of a Cohen-Grossberg neural network system with nonnegative equilibria

In: Neural networks, 20 (2007) 6, pp. 714-722