1.

Hopfield, J.J.: Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. U.S.A. **81**, 3088–3092 (1984)

2.

Hale, J., Lenel, S.V.: Introduction to Functional Differential Equations. Springer, New York (1993)

3.

Gopalsamy, K.: Stability and Oscillations in Delay Differential Equations of Populations Dynamics. Kluwer, Dordrecht, The Netherlands (1992)

4.

Marcus, C.M., Westervelt, R.M.: Stability of analog neural networks with delay. Phys. Rev. A

**39**, 347–359 (1989)

CrossRefMathSciNet5.

Baldi, P., Atiya, A.F.: How delays affect neural dynamics and learning. IEEE Trans. Neural Network

**5**, 612–621 (1994)

CrossRef6.

Olien, L., Belair, J.: Bifurcation, stability and monotonicity properties of a delayed neural model. Physica D

**102**, 349–363 (1997)

MATHCrossRefMathSciNet7.

Belair, J., Dufour, S.: Stability in a three-dimensional system of delay-differential equations. Can. Appl. Math. Quart. **4**, 1878–1890 (1998)

8.

Gopalsamy, K., He, X.: Delay-independent stability in bi-directional associative memory networks. IEEE Trans. Neural Network

**5**, 998–1002 (1994)

CrossRef9.

Gopalsamy, K., Leung, I.: Delay-induced periodicity in a neural network of excitation and inhibition. Physica D

**89**, 395–426 (1996)

MATHCrossRefMathSciNet10.

Gopalsamy, K., Leung, I.: Convergence under dynamical thresholds with delays. IEEE Trans. Neural Network **8**(2), 341–348 (1997)

11.

Gopalsamy, K., Leung, I., Liu, P.: Global Hopf-bifurcation in a neural netlet. Appl. Math. Comput. **94**, 171–192 (1998)

12.

Wei, J., Ruan, S.: Stability and bifurcation in a neural network model with two delays. Physica D

**130**, 255–272 (1999)

MATHCrossRefMathSciNet13.

Babcock, K.L., Westervelt, R.M.: Dynamics of simple electronic neural networks with added inertia. Physica D

**23**, 464–469 (1986)

CrossRef14.

Babcock, K.L., Westervelt, R.M.: Dynamics of simple electronic neural networks. Physica D

**28**, 305–316 (1987)

CrossRefMathSciNet15.

Destxhe, A.: Stability of periodic oscillation in a network of neurons with time delay. Phys. Lett. A

**187**, 309–316 (1994)

CrossRef16.

Campbell, S.A.: Stability and bifurcation of a simple neural network with multiple time delays. Fields Inst. Commun. **21**, 65–79 (1999)

17.

An der Heiden, U.: Delays in physiological systems. J. Math. Biol.

**8**, 345–364 (1979)

MATHMathSciNet18.

Willson, H.R., Cowan, J.D.: Excitatory and inhibitory interactions in locallized populations of model neurons. Biophys. J.

**12**, 1–24 (1972)

CrossRef19.

Destexhe, A., Gaspard, P.: Bursting oscillations from a homoclinic tangency in a time delat system. Phys. Lett. A

**173**, 386–391 (1993)

CrossRef20.

Majee, N.C., Roy, A.B.: Temporal dynamics of a two-neuron continuous network model with time delay. Appl. Math. Model.

**21**, 673–679 (1997)

MATHCrossRef21.

Liao, X.F., Wu, Z.F., Yu, J.B.: Stability switches and bifurcation analysis of a neural network with continuously delay. IEEE Trans. Syst. Man Cybernet.

**29**, 692–696 (1999)

CrossRef22.

Liao, X.F., Wong, K.W., Leung, C.S., Wu, Z.F.: Hopf bifurcation and chaos in a single delayed neuron equation with nonmonotonic activation function. Chaos Solitons Fractals

**21**, 1535–1547 (2001)

CrossRefMathSciNet23.

Liao, X.F., Wong, K.W., Wu, Z.F.: Bifurcation analysis in a two-neuron system with distributed delays. Physica D

**149**, 123–141 (2001)

MATHCrossRefMathSciNet24.

Liao, X.F., Wong, K.W., Wu, Z.F.: Asymptotic stability criteria for a two-neuron network with different time delays. IEEE Trans. Neural Network **14**(1), 222–227 (2003)

25.

Liao, X.F., Yu, J.B.: Robust interval stability analysis of Hopfield networks with time delays. IEEE Trans. Neural Network

**9**, 1042–1045 (1998)

CrossRef26.

Liao, X.F., Wong, K.W., Wu, Z.F., Chen, G.: Novel robust stability criteria for interval delayed Hopfield neural networks with time delays. IEEE Tran. Syst. I **48**, 1355–1359 (2001)

27.

Liao, X.F., Yu, J.B., Chen, G.: Novel stability conditions for cellular neural networks with time delays. Int. J. Bif. Chaos **11**(7), 1853–1864 (2001)

28.

Liao, X.F., Chen, G., Sanchez, E.N.: LMI-based approach for asymptotically stability analysis of delayed neural networks. IEEE Trans. Circuits Syst. I

**49**, 1033–1039 (2002)

CrossRefMathSciNet29.

Liao, X.F., Chen, G., Sanchez, E.N.: Delay-dependent exponential stability analysis of delayed neural networks: An LMI approach. Neural Network

**15**, 855–866 (2002)

CrossRef30.

Liao, X.F., Li, S.W., Chen, G.: Bifurcation analysis on a two-neuron system with distributed delays in the frequency domain. Neural Network **17**(4), 545–561 (2004)

31.

Liao, X.F., Wong, K.W.: Robust stability of interval bi-directional associative menmory neural networks with time delays. IEEE Trans. Man Cybernet. B **34**(2), 1141–1154 (2004)

32.

Liao, X.F., Wong, K.W.: Global exponential stability for a class of retarded functional differential equations with applications in neural networks. J. Math. Anal. Appl. **293**(1), 125–148 (2004)

33.

Liao, X.F., Li, C.G., Wong, K.W.: Criteria for exponential stability of Cohen–Grossberg neural networks. Neural Network

**17**, 1401–1414 (2004)

MATHCrossRef34.

Liao, X.F., Wong, K.W., Yang, S.Z.: Stability analysis for delayed cellular neural networks based on linear matrix inequality approach. Int. J. Bif. Chaos.

**14**(9), 3377–3384 (2004)

MATHCrossRefMathSciNet35.

Liao, X.F., Li, C.D.: An LMI approach to asymptotical stability of multi-delayed neural networks. Physica D **200**(1–2), 139–155 (2005)

36.

Liao, X.F., Wu, Z.F., Yu, J.B.: Hopf bifurcation analysis of a neural system with a continuously distributed delay. In: Proceeding of the International Symposium on Signal Processing and Intelligent System, Guangzhou, China (1999)

37.

Pakdaman, K., Malta, C.P., et al.: Transient oscillations in continuous-time excitatory ring neural networks with delay. Phys. Rev. E

**55**, 3234–3248 (1997)

CrossRefMathSciNet38.

Van Den Driessche, P., Zou, X.: Global attractivity in delayed Hopfield neural networks model. SIAM J. Appl. Math.

**58**, 1878–1890 (1998)

MATHCrossRefMathSciNet39.

Giannakopoulos, F., Zapp, A.: Bifurcations in a planar system of differential delay equations modeling neural activity. Physica D **159**(3–4), 215–232 (2001)

40.

Liu, B., Huang, L.: Periodic solutions for a two-neuron network with delays. Nonlinear Anal. Real World Appl.

**7**(4), 497–509 (2006)

MATHCrossRefMathSciNet41.

Li, C.G., Chen, G., Liao, X.F., Yu, J.B.: Hopf bifurcation and chaos in Tabu learning neuron models. Int. J. Bif. Chaos

**15**(8), 2633–2642 (2005)

MATHCrossRefMathSciNet42.

Wei, J., Ruan, S.: Stability and bifurcation in a neural network model with two delays. Physica D

**130**(1–2), 255–272 (1999)

MATHCrossRefMathSciNet43.

Hassard, B.D., Kazarinoff, N.D., Wan, Y.H.: Theory and Applications of Hopf Bifurcation. Cambridge University Press, Cambridge (1981)