Asymptotic behavior of periodic Cohen-Grossberg neural networks with delays

Authors:
Wei Lin
Affiliations:
Department of Mathematics, University of Southern California, Los Angeles, CA
Venue:
Neural Computation
Year:
2009

Citing 6
Cited 0

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

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Robust global exponential stability of Cohen-Grossberg neural networks with time delays

IEEE Transactions on Neural Networks

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Abstract

Without assuming the positivity of the amplification functions, we prove some M-matrix criteria for the R+n -global asymptotic stability of periodic Cohen-Grossberg neural networks with delays. By an extension of the Lyapunov method, we are able to include neural systems with multiple nonnegative periodic solutions and nonexponential convergence rate in our model and also include the Lotka-Volterra system, an important prototype of competitive neural networks, as a special case. The stability criteria for autonomous systems then follow as a corollary. Two numerical examples are provided to show that the limiting equilibrium or periodic solution need not be positive.