## Exponential stability of delayed bi-directional associative memory networks.(English)Zbl 1030.34073

Summary: Some sufficient conditions are derived for the global exponential stability in delayed bi-directional associative memory (BAM) networks by constructing a suitable Lyapunov functional and the inequality $$2ab\leq a^2+b^2$$ technique. These conditions have an important leading significance in the design and applications of globally exponentially stable neural circuits for delayed BAM.

### MSC:

 34K20 Stability theory of functional-differential equations 34K60 Qualitative investigation and simulation of models involving functional-differential equations 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 92B20 Neural networks for/in biological studies, artificial life and related topics

### Keywords:

suitable Lyapunov functional
Full Text:

### References:

 [1] Kosko, B., (), 38-108 [2] Kosko, B., Bi-directional associative memories, IEEE trans. syst. man cybernet., 18, 1, 49-60, (1988) [3] Kosko, B., Adaptive bi-directional associative memories, Appl. opt., 26, 23, 4947-4960, (1987) [4] Gopalsamy, K.; He, X.Z., Delay-independent stability in bi-directional associative memory networks, IEEE trans. neural networks, 5, 998-1002, (1994) [5] Liao, X.F.; Liu, G.Y.; Yu, J.B., Neural networks of bi-directional associative memory with axonal signal transmission delays, J. electron., 19, 4, 439-444, (1997), (in Chinese) [6] Cao, J.D.; Wang, L., Periodic oscillatory solution of bidirectional associative memory networks with delays, Phys. rev. E, 61, 2, 1825-1828, (2000) [7] Zhang, Y., Qualitative analysis of bi-directional associative memory neural networks with delays, J. comput. res. dev., 36, 2, 150-155, (1999), (in Chinese) [8] Liao, X.F.; Liu, G.Y.; Yu, J.B., Qualitative analysis of continuous bi-directional associative memory model, J. circuits syst., 2, 2, 13-18, (1996), (in Chinese) [9] Kohonen, T., Self-organization and associative memory, (1988), Springer New York · Zbl 0659.68100 [10] Liao, X.F.; Yu, J.B., Qualitative analysis of bi-directional associative memory with time delay, Int. J. circuit theory appl., 26, 3, 219-229, (1998) · Zbl 0915.94012 [11] Kleinfeld, D., Sequential state generation by model neural networks, Proc. nat. acad. sci. USA, 83, 9469-9473, (1986) [12] Kelly, D.G., Stability in contractive nonlinear neuralnetworks, IEEE trans. biomed. eng., 37, 3, 231-242, (1990) [13] Michel, A.N.; Farrel, J.A.; Porod, W., Qualitative analysis of neural networks, IEEE trans. circuits syst., 36, 229-244, (1989) [14] Cao, J.D., Global stability analysis in delayed cellular neural networks, Phys. rev. E, 59, 5, 5940-5944, (1999) [15] Cao, J.D.; Zhou, D.M., Stability analysis of delayed cellular neural networks, Neural networks, 11, 9, 1601-1605, (1998) [16] Cao, J.D., Periodic solutions and exponential stability in delayed cellular neural networks, Phys. rev. E, 60, 3, 3244-3248, (1999) [17] Cao, J.D., On stability of delayed cellular neural networks, Phys. lett. A, 261, 56, 303-308, (1999) · Zbl 0935.68086 [18] Cao, J.D., Global exponential stability and periodic solutions of delayed cellular neural networks, J. comput. syst. sci. (USA), 60, 1, 38-46, (2000) · Zbl 0988.37015 [19] Yang, H.; Dillon, T.S., Exponential stability and oscillation of Hopfield graded response neural networks, IEEE trans. neural networks, 5, 719-729, (1994) [20] Cao, J.D.; Li, J.B., The stability in neural networks with interneuronal transmission delays, Appl. math. mech., 19, 5, 457-462, (1998) · Zbl 0908.92003 [21] Cao, J.D., Stability analysis of Hopfield neural networks, (), 1291-1294 [22] Marcus, C.M.; Westervelt, R.M., Stability of analogy neural networks with delay, Phys. rev. A, 39, 347-359, (1989) [23] Cao, J.D.; Wan, S.D., The global asymptotic stability of Hopfield neural network with delays, J. biomath., 12, 1, 60-63, (1997), (in Chinese) · Zbl 0891.92001 [24] Cao, J., A set of stability criteria for delayed cellular neural networks, IEEE trans. circuits syst. I, 48, 4, 494-498, (2001) · Zbl 0994.82066 [25] Cao, J., Corrections to “A set of stability criteria for delayed cellular networks”, IEEE trans. circuits syst. I, 48, 10, 1267, (2001) [26] Cao, J., Global stability conditions for delayed cnns, IEEE trans. circuits syst. I, 48, 11, 1330-1333, (2001) · Zbl 1006.34070 [27] Cao, J., On exponential stability and periodic solutions of CNNs with delays, Phys. lett. A, 267, 6-7, 312-318, (2000) · Zbl 1098.82615 [28] Cao, J., Periodic oscillation and exponential stability of delayed cnns, Phys. lett. A, 270, 2-4, 157-163, (2000) [29] Cao, J., Exponential stability and periodic solution of delayed cellular neural networks, Science in China (series E), 43, 3, 328-336, (2000) · Zbl 1019.94041 [30] J. Cao, L. Wang, Exponential stability and periodic oscillatory solution in BAM networks with delays, IEEE Trans. Neural Networks, in press
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