Analysis for Cohen-Grossberg neural networks with multiple delays

Ji, Ce; Zhang, Huaguang; Guan, Huanxin; Ping, Yuan

doi:10.1007/s11768-006-4199-z

Cited by 3 publications

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“…In reality, during the implementation of artificial neural networks on very large scale integrated circuit, transmitting time delays due to the finite switching speed of amplifiers are unavoidable and may lead to instability and oscillation in a neural network. For this reason, some works have shown that time delays should be incorporated into the model equations of the network (for example, [8][9][10][11][12][13]). In [8], Cao and Liang proposed a Cohen-Grossberg neural network with time-varying delays.…”

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Stability and Hopf bifurcation of a delayed Cohen–Grossberg neural network with diffusion

Tian

2016

Math Methods in App Sciences

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In this paper, a delayed Cohen-Grossberg neural network with diffusion under homogeneous Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equation, the local stability of the trivial uniform steady state and the existence of Hopf bifurcation at the trivial steady state are established, respectively. By using the normal form theory and the center manifold reduction of partial function differential equations, formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results.The Cohen-Grossberg neural network is a general neural network model that includes Hopfield-type neural network and cellular neural network as its special cases. Recently, great attention has been paid to Cohen-Grossberg neural network, and it has been successfully applied to many areas, such as control, image processing, pattern recognition, parallel computation, associative memories, and optimization (for example, [2][3][4][5][6][7]).In the previous works, the effect of time delay was ignored in most models. In reality, during the implementation of artificial neural networks on very large scale integrated circuit, transmitting time delays due to the finite switching speed of amplifiers are unavoidable and may lead to instability and oscillation in a neural network. For this reason, some works have shown that time delays should be incorporated into the model equations of the network (for example, [8][9][10][11][12][13]). In [8], Cao and Liang proposed a Cohen-Grossberg neural network with time-varying delays. By combining the Halanay inequality with the Lyapunov functional method, sufficient conditions were derived for the model to be globally and exponentially stable. In [13], Zhu and Cao developed a linear matrix inequality to derive 2 ja 1 a 2 d 1 d 2 g 0 1 g 0 2 j > 0.Therefore, Eq. (2.7) with k 2 N 0 nfk 0 g has no purely imaginary roots.

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