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Existence and global convergence of periodic solution of delayed neural networks. (English) Zbl 1145.34366
Summary: This paper is concerned with the existence and global convergence of a periodic solution of delayed neural networks. Employing Schauder fixed point theorem, we obtain some novel sufficient conditions ensuring the existence as well as the global convergence of the periodic solution. Our results are new and improve some previously known results since these results are based on integral average values of the coefficients. The theoretical analysis is verified by numerical simulations.

34K13 Periodic solutions to functional-differential equations
37N25 Dynamical systems in biology
Full Text: DOI
[1] Arik, S., Stability analysis of delayed neural networks, IEEE trans. circuits and syst. I: fundamental theory and applications, 47, 1089-1092, (2000) · Zbl 0992.93080
[2] Cao, J., Global stability analysis in delayed cellular neural networks, Phys. rev. E, 59, 5940-5944, (1999)
[3] Cao, J.; Wang, J., Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays, Neural netw., 17, 379-390, (2004) · Zbl 1074.68049
[4] Chen, T., Global exponential stability of delayed Hopfield neural networks, Neural netw., 14, 977-1143, (2001)
[5] van den Driessche, P.; Zou, X., Global attractivity in delayed Hopfield neural network models, SIAM J. appl. math., 58, 1878-1890, (1998) · Zbl 0917.34036
[6] Forti, M., On global asymptotic stability of a class of nonlinear systems arising in neural network theory, J. differential equations, 113, 246-264, (1994) · Zbl 0828.34039
[7] Gopalsamy, K.; He, X., Delay-independent stability in bidirectional associative memory networks, IEEE trans. neural networks, 5, 998-1022, (1994)
[8] Huang, C.; Huang, L.; Yuan, Z., Global stability analysis of a class of delayed cellular neural networks, Math. comput. simulation, 70, 133-148, (2005) · Zbl 1094.34052
[9] Hwang, C.C.; Chen, C.J.; Liao, T.L., Globally exponential stability of generalized cohen – grossberg neural networks with delays, Phys. lett. A, 319, 157-166, (2003) · Zbl 1073.82597
[10] Joy, M., Results concerning the absolute stability of delayed neural networks, Neural netw., 13, 613-616, (2000)
[11] Li, X.; Huang, L.; Zhu, H., Global stability of cellular neural networks with constant and variable delays, Nonlinear anal., 53, 319-333, (2003) · Zbl 1011.92006
[12] Liao, X.; Wong, K., Global exponential stability for a class of retarded functional differential equations with applications in neural networks, J. math. anal. appl., 293, 125-148, (2004) · Zbl 1059.34052
[13] Marcus, C.M.; Westervelt, R.M., Stability of analog neural networks with delay, Phys. rev. A, 39, 347-359, (1989)
[14] Roska, T.; Chua, L.O., Cellular neural networks with nonlinear and delay type template elements and non-uniform grids, Int. J. circuit theory appl., 20, 469-481, (1992) · Zbl 0775.92011
[15] Roska, T.; Wu, C.W.; Chua, L.O., Stability of cellular neural networks with dominant nonlinear and delay-type templates, IEEE trans. circuits syst., 40, 270-272, (1993) · Zbl 0800.92044
[16] Wang, L., Stabilizing Hopfield neural networks via inhibitory self-connections, J. math. anal. appl., 292, 135-147, (2004) · Zbl 1062.34087
[17] Wu, J., Introduction to neural dynamics and signal transmission delay, (2001), Walter de Gruyter Berlin · Zbl 0977.34069
[18] Yuan, Z.; Hu, D.; Huang, L.; Dong, G., On the global asymptotic stability analysis of delayed neural networks, Inter. J. bifur. chaos, 15, 4019-4025, (2005) · Zbl 1093.92010
[19] Chen, A.; Huang, L.; Liu, Z.; Cao, J., Periodic bidirectional associative memory neural networks with distributed delays, J. math. anal. appl., 317, 80-102, (2006) · Zbl 1086.68111
[20] Dong, Q.; Matsui, K.; Huang, X., Existence and stability of periodic solutions for Hopfield neural network equations with periodic input, Nonlinear anal., 49, 471-479, (2002) · Zbl 1004.34065
[21] Huang, L.; Huang, C.; Liu, B., Dynamics of a class of cellular neural networks with time-varying delays, Phys. lett. A, 345, 330-344, (2005) · Zbl 1345.92014
[22] Yuan, Z.; Huang, L.; Hu, D.; Dong, G., Existence and global exponential stability of periodic solution for Cohen-Grossberg neural networks with delays, Nonlinear anal. RWA, 7, 572-590, (2006) · Zbl 1114.34053
[23] Yuan, Z.; Yuan, L.; Huang, L., Dynamics of periodic Cohen-Grossberg neural networks with varying delays, Neurocomputing, 70, 164-172, (2006)
[24] Zheng, Y.; Chen, T., Global exponential stability of delayed periodic dynamical systems, Phys. lett. A, 322, 344-355, (2004) · Zbl 1118.81479
[25] Zhou, T.; Chen, A.; Zhou, Y., Existence and global exponential stability of periodic solution to BAM neural networks with periodic coefficients and continuously distributed delays, Phys. lett. A, 343, 336-350, (2005) · Zbl 1194.34134
[26] Zhou, J.; Liu, Z.; Chen, G., Dynamics of periodic delayed neural networks, Neural netw., 17, 87-101, (2004) · Zbl 1082.68101
[27] Berman, A.; Plemmons, R.J., Nonnegative matrixes in mathematical science, (1979), Academic Press New York
[28] Zeidler, E., Applied functional analysis: applications to mathematical physics, (1995), Springer-Verlag New York · Zbl 0834.46002
[29] Roydin, H.L., Real analysis, (1988), Macmillan Publishing Company New York
[30] Shampine, L.F.; Thompson, S., Solving DDEs in Matlab, Appl. numer. math., 37, 441-458, (2001) · Zbl 0983.65079
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