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Existence and exponential stability of periodic solutions for a class of Cohen-Grossberg neural networks with bounded and unbounded delays. (English) Zbl 1121.68097
Summary: This paper is concerned with existence and global exponential stability of periodic solutions for a class of Cohen-Grossberg neural networks with bounded and unbounded delays. By the continuation theorem of coincidence degree theory and differential inequality techniques, we deduce some sufficient conditions ensuring existence as well as global exponential stability of periodic solution. These conditions in our results are milder and less restrictive than that of previous known criteria since the hypothesis of boundedness and differentiability on the activation function are dropped. The theoretical analysis are verified by numerical simulations.

MSC:
68T05 Learning and adaptive systems in artificial intelligence
Software:
dde23
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[1] Cohen, M.; Grossberg, S., Absolute stability and global pattern formation and parallel memory storage by competitive neural networks, IEEE trans. man cybernet., SMC, 13, 815-826, (1983) · Zbl 0553.92009
[2] Gopalsamy, K.; He, X.Z., Delay-independent stability in bidirection associative memory networks, IEEE trans. neural networks, 5, 998-1002, (1994)
[3] 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
[4] Guo, S.; Huang, L., Stability analysis of a delayed Hopfield neural network, Phys. rev. E, 67, 061902, (2003)
[5] Cao, J., Global stability analysis in delayed cellular neural networks, Phys. rev. E, 59, 5940-5944, (1999)
[6] Wang, L.; Zou, X., Harmless delays in cohen – grossberg neural networks, Physica D, 170, 162-173, (2002) · Zbl 1025.92002
[7] Cao, J.; Liang, J., Boundedness and stability for cohen – grossberg neural networks with time-varying delays, J. math. anal. appl., 296, 665-685, (2004) · Zbl 1044.92001
[8] Chen, T.; Rong, L., Delay-independent stability analysis of cohen – grossberg neural networks, Phys. lett. A, 317, 436-449, (2003) · Zbl 1030.92002
[9] Li, Y., Existence and stability of periodic solutions for cohen – grossberg neural networks with multiple delays, Chaos solitons fractals, 20, 459-466, (2004) · Zbl 1048.34118
[10] Liao, X.; Li, C.; Wong, K., Criteria for exponential stability of cohen – grossberg neural networks, Neural netw., 17, 1401-1414, (2004) · Zbl 1073.68073
[11] Wang, L., Stability of cohen – grossberg neural networks with distributed delays, Appl. math. comput., 160, 93-110, (2005) · Zbl 1069.34113
[12] Wang, L.; Zou, X., Exponential stability of cohen – grossberg neural networks, Neural netw., 15, 415-422, (2002)
[13] Kennedy, M.P.; Chua, L.O., Neural networks for nonlinear programming, IEEE trans. syst., 35, 554-562, (1988)
[14] Morita, M., Associative memory with nonmonotone dynamics, Neural netw., 6, 115-126, (1993)
[15] Liu, Z.; Liao, L., Existence and global exponential stability of periodic solution of cellular neural networks with time-varying delays, J. math. anal. appl., 290, 247-262, (2004) · Zbl 1055.34135
[16] 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
[17] Yuan, Z.; Yuan, L.; Huang, L., Dynamics of periodic cohen – grossberg neural networks with varying delays, Neurocomputing, 70, 164-172, (2006)
[18] Gaines, R.E.; Mawhin, J.L., Coincidence degree, and nonlinear differential equations, (1977), Springer-Verlag Berlin · Zbl 0326.34021
[19] LaSalle, J.P., The stability of dynamical system, (1976), SIAM Philadelphia · Zbl 0364.93002
[20] Berman, A.; Plemmons, R.J., Nonnegative matrices in the mathematical science, (1979), Academic Press New York
[21] Shampine, L.F.; Thompson, S., Solving DDEs in Matlab, Appl. numer. math., 37, 441-458, (2001) · Zbl 0983.65079
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