##
**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
PDF
BibTeX
XML
Cite

\textit{J. Cao} and \textit{M. Dong}, Appl. Math. Comput. 135, No. 1, 105--112 (2003; Zbl 1030.34073)

Full Text:
DOI

### 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 networksâ€ť, 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 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.