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Stability in asymmetric Hopfield nets with transmission delays. (English) Zbl 0815.92001
Summary: Sufficient conditions are derived for the delay independent stability of the equilibria in Hopfield’s graded response networks of the type \[ dx_ i (t)/dt = - b_ i x_ i(t) + \sum^ n_{j=1} a_{ij}f_ j \bigl( \mu_ j x_ j(t - \tau_{ij}) \bigr) + F_ i(t) \quad (i = 1,2, \dots,n) \] when the external inputs \(F_ i\) are held temporally uniform. A generalization to continuously distributed delays is briefly indicated. Several illustrative examples are numerically simulated and the results of simulations are graphically displayed.

92B20 Neural networks for/in biological studies, artificial life and related topics
34D99 Stability theory for ordinary differential equations
Full Text: DOI
[1] Barbalat, I., Systemes d’equations differentielle d’oscillations nonlineaires, Rev. roumaine math. pures appl., 4, 267-270, (1959) · Zbl 0090.06601
[2] Carpenter, G.A.; Cohen, M.; Grosberg, S., Computing with neural networks, Science, 235, 1226-1227, (1987)
[3] Cohen, M.A.; Grossberg, S., Absolute stability and global pattern formation and parallel memory storage by competitive neural networks, IEEE. trans. syst. man. cybern. SMC, 13, 815-821, (1983) · Zbl 0553.92009
[4] Forti, M.; Manetti, S.; Marini, M., A condition for global convergence of a class of symmetric neural circuits, IEEE trans. circ. syst., 39, 480-483, (1992) · Zbl 0775.92005
[5] Gopalsamy, K., Stability and oscillations in delay differential equations of population dynamics, (1992), Kluwer Dordrecht · Zbl 0752.34039
[6] K. Gopalsamy and X.Z. He, Delay independent stability in bidirectional associative memory networks, IEEE Trans. Neural Networks, in press.
[7] Hopfield, J., Neurons with graded response have collective computational properties like those of two sate neurons, (), 3088-3092 · Zbl 1371.92015
[8] Kelly, D.G., Stability in contractive nonlinear neural networks, IEEE trans. biomed. engin., 37, 231-242, (1990)
[9] Kuhn, R.; Van Hemmen, J.L., ()
[10] Hua, Li Jian; Michel, A.N.; Porod, W., Qualitative analysis and synthesis of a class of neural networks, IEEE. trans. circ. syst., 35, 976-986, (1988) · Zbl 0664.34042
[11] Marcus, C.M.; Westervelt, R.M., Dynamics of analog neural networks with time delay, (), 568-576
[12] Marcus, C.M.; Westervelt, R.M., Stability of analog neural networks with time delay, Phys. rev. A, 39, 347-359, (1989)
[13] Matsuoka, K., Stability conditions for nonlinear continuous neural networks with asymptotic connection weights, Neural networks, 5, 495-500, (1992)
[14] Scott, A.C., Neurophysics, (1977), Wiley-Interscience New York
[15] Tank, D.W.; Hopfield, J.J., Neural computation by concentrating in information in time, (), 1896-1991 · Zbl 0572.68041
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