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

Wenlian Lu, and Tianping Chen
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Submission date: 30. Jun. 2007
Pages: 28
published in: Neural networks, 20 (2007) 6, p. 714-722 
DOI number (of the published article): 10.1016/j.neunet.2007.05.004
MSC-Numbers: 34D23, 34K20
Keywords and phrases: Cohen Grossberg neural networks, nonnegative equilibrium, $R^{n}_{+}$ global stability
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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 -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.