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Articles accepted for publication will be licensed under the Creative Commons BY-NC. Authors must sign a non-exclusive distribution agreement after article acceptance.

- Xuyang Lou Research Center of Control Science and Engineering, Jiangnan University, 1800 Lihu Rd.,Wuxi, Jiangsu 214122, P.R.China
- Baotong Cui Research Center of Control Science and Engineering, Jiangnan University, 1800 Lihu Rd.,Wuxi, Jiangsu 214122, P.R.China

The exponential periodicity and stability of continuous nonlinear neural networks with variable coefficients and distributed delays are investigated via employing Young inequality technique and Lyapunov method. Some new sufficient conditions ensuring existence and uniqueness of periodic solution for a general class of neural systems are obtained. Without assuming the activation functions are to be bounded, differentiable or strictly increasing. Moreover, the symmetry of the connection matrix is not also necessary. Thus, we generalize and improve some previous works, and they are easy to check and apply in practice.

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[1] J. D. Cao. A set of stability criteria for delayed cellular neural networks, IEEE Trans. Circuits Syst. I, vol. 48, pp. 494-498, 2001.

[2] J. D. Cao and D. M. Zhou. Stability analysis of delayed cellular neural networks, Neural Networks, vol. 11, no. 9, pp. 1601-1605, 1998.

[3] S. Arik and V. Tavsanoglu. Equilibrium analysis of delayed CNNs, IEEE Trans. Circuits Syst. I, vol. 45, pp. 168-171, 1998.

[4] X. Liao et al. Novel robust stability for interval-delayed Hopfield neural networks, IEEE Trans. Circuits Syst. I, vol. 48, pp. 1355-1359, 2001.

[5] J. D. Cao. Periodic oscillation and exponential stability of delayed CNNs, Phys. Lett. A, vol. 270, no. 3-4, pp. 157-163, 2000.

[6] S. Arik. Global robust stability of delayed neural networks, IEEE Trans. Circuits Syst. I, vol. 50, no. 1, pp. 156-160, 2003.

[7] S. Arik and V. Tavsanoglu. On the global asymptotic stability of delayed cellular neural networks, IEEE Trans. Circuits Syst. I, vol. 47, no. 4, pp. 571-574, 2000.

[8] X.Y. Lou, B.T. Cui, New criteria on global exponential stability of BAM neural networks with distributed delays and reaction-diffusion terms, International Journal of Neural Systems, vol. 17, no. 1, pp. 43-52, 2007.

[9] Z. G. Liu, A. P. Chen, J. D. Cao and L. H. Huang. Existence and global exponential stability of periodic solution for BAM neural networks with periodic coefficients and time-varying delays, IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 50, no. 9, pp. 1162-1173, 2003.

[10] J. D. Cao and L. Wang. Exponential stability and periodic oscillatory solution in BAM networks with delays, IEEE Transactions on Neural Networks, vol. 13, no. 2, pp. 457-463, 2002.

[11] J. D. Cao. Global stability conditions for delayed CNNS, IEEE Trans. Circuits Syst. I, vol. 48, pp. 1330-1333, 2001.

[12] S. Xu and J. Lam. A new approach to exponential stability analysis of neural networks with time-varying delays, Neural Networks, vol. 19, no. 1, pp. 76-83, 2006.

[13] X. Y. Lou, B. T. Cui. New LMI conditions for delay-dependent asymptotic stability of delayed Hopfield neural networks, Neurocomputing, vol. 69, no. 16-18, pp. 2374-2378, 2006.

[14] J. D. Cao. Global Exponential Stability and Periodic Solutions of Delayed Cellular Neural Networks, Journal of Computer and Systems Sciences, vol. 60, pp. 38-46, 2000.

[15] Q. K. Song and J. D. Cao. Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction-diffusion terms, Chaos, Solitons and Fractals, vol. 23, pp. 421-430, 2005.

[16] Y. K. Li. Existence and stability of periodic solution for BAM neural networks with distributed delays, Applied Mathematics and Computation, vol. 159, pp. 847-862, 2004.

[17] K. Matsuoka. Stability conditions for nonlinear continuous neural networks with asymmetric connection weights, Neural Networks, vol. 5, no. 3, pp. 495-500, 1992.

[18] X. Y. Lou and B. T. Cui. Global asymptotic stability of delay BAM neural networks with impulses, Chaos, Solitons and Fractals, vol. 29, no. 4, pp. 1023-1031, 2006.

[19] X. Y. Lou and B. T. Cui. Absolute exponential stability analysis of delayed bi-directional associative memory neural networks, Chaos, Solitons and Fractals, vol. 31, no. 3, pp. 695-701, 2007.

[20] H. T. Lu. On stability of nonlinear continuous-time neural networks with delays, Neural Networks, vol. 13, no. 10, pp. 1135-1143, 2000.

[21] C. Y. Sun and C. B. Feng. Exponential periodicity and stability of delayed neural networks, Mathematics and Computers in Simulation, vol. 66, pp. 469-478, 2004.

[22] H. Huang, D. W. C. Ho and J. D. Cao. Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays, Neural Networks, vol. 18, no. 2, pp. 161-170, 2005.

[23] K. Gopalsamy and X. Z. He. Stability in asymmetric Hopfield nets with transmission delays, Physica D, vol. 76, pp. 344-358, 1994.

[24] S. Mohamad and K. Gopalsamy. Dynamics of a class of discrete-time neural networks and their continuous-time counterparts, Math. Comput. Simulation, vol. 53, no. 1-2, pp. 1-39, 2000

[2] J. D. Cao and D. M. Zhou. Stability analysis of delayed cellular neural networks, Neural Networks, vol. 11, no. 9, pp. 1601-1605, 1998.

[3] S. Arik and V. Tavsanoglu. Equilibrium analysis of delayed CNNs, IEEE Trans. Circuits Syst. I, vol. 45, pp. 168-171, 1998.

[4] X. Liao et al. Novel robust stability for interval-delayed Hopfield neural networks, IEEE Trans. Circuits Syst. I, vol. 48, pp. 1355-1359, 2001.

[5] J. D. Cao. Periodic oscillation and exponential stability of delayed CNNs, Phys. Lett. A, vol. 270, no. 3-4, pp. 157-163, 2000.

[6] S. Arik. Global robust stability of delayed neural networks, IEEE Trans. Circuits Syst. I, vol. 50, no. 1, pp. 156-160, 2003.

[7] S. Arik and V. Tavsanoglu. On the global asymptotic stability of delayed cellular neural networks, IEEE Trans. Circuits Syst. I, vol. 47, no. 4, pp. 571-574, 2000.

[8] X.Y. Lou, B.T. Cui, New criteria on global exponential stability of BAM neural networks with distributed delays and reaction-diffusion terms, International Journal of Neural Systems, vol. 17, no. 1, pp. 43-52, 2007.

[9] Z. G. Liu, A. P. Chen, J. D. Cao and L. H. Huang. Existence and global exponential stability of periodic solution for BAM neural networks with periodic coefficients and time-varying delays, IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 50, no. 9, pp. 1162-1173, 2003.

[10] J. D. Cao and L. Wang. Exponential stability and periodic oscillatory solution in BAM networks with delays, IEEE Transactions on Neural Networks, vol. 13, no. 2, pp. 457-463, 2002.

[11] J. D. Cao. Global stability conditions for delayed CNNS, IEEE Trans. Circuits Syst. I, vol. 48, pp. 1330-1333, 2001.

[12] S. Xu and J. Lam. A new approach to exponential stability analysis of neural networks with time-varying delays, Neural Networks, vol. 19, no. 1, pp. 76-83, 2006.

[13] X. Y. Lou, B. T. Cui. New LMI conditions for delay-dependent asymptotic stability of delayed Hopfield neural networks, Neurocomputing, vol. 69, no. 16-18, pp. 2374-2378, 2006.

[14] J. D. Cao. Global Exponential Stability and Periodic Solutions of Delayed Cellular Neural Networks, Journal of Computer and Systems Sciences, vol. 60, pp. 38-46, 2000.

[15] Q. K. Song and J. D. Cao. Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction-diffusion terms, Chaos, Solitons and Fractals, vol. 23, pp. 421-430, 2005.

[16] Y. K. Li. Existence and stability of periodic solution for BAM neural networks with distributed delays, Applied Mathematics and Computation, vol. 159, pp. 847-862, 2004.

[17] K. Matsuoka. Stability conditions for nonlinear continuous neural networks with asymmetric connection weights, Neural Networks, vol. 5, no. 3, pp. 495-500, 1992.

[18] X. Y. Lou and B. T. Cui. Global asymptotic stability of delay BAM neural networks with impulses, Chaos, Solitons and Fractals, vol. 29, no. 4, pp. 1023-1031, 2006.

[19] X. Y. Lou and B. T. Cui. Absolute exponential stability analysis of delayed bi-directional associative memory neural networks, Chaos, Solitons and Fractals, vol. 31, no. 3, pp. 695-701, 2007.

[20] H. T. Lu. On stability of nonlinear continuous-time neural networks with delays, Neural Networks, vol. 13, no. 10, pp. 1135-1143, 2000.

[21] C. Y. Sun and C. B. Feng. Exponential periodicity and stability of delayed neural networks, Mathematics and Computers in Simulation, vol. 66, pp. 469-478, 2004.

[22] H. Huang, D. W. C. Ho and J. D. Cao. Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays, Neural Networks, vol. 18, no. 2, pp. 161-170, 2005.

[23] K. Gopalsamy and X. Z. He. Stability in asymmetric Hopfield nets with transmission delays, Physica D, vol. 76, pp. 344-358, 1994.

[24] S. Mohamad and K. Gopalsamy. Dynamics of a class of discrete-time neural networks and their continuous-time counterparts, Math. Comput. Simulation, vol. 53, no. 1-2, pp. 1-39, 2000

2007-10-01

Original Articles

Articles accepted for publication will be licensed under the Creative Commons BY-NC. Authors must sign a non-exclusive distribution agreement after article acceptance.

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