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Global asymptotic stability of Cohen-Grossberg neural network with continuously distributed delays. (English) Zbl 1222.93200
Summary: The convergence dynamical behaviors of Cohen-Grossberg neural network with continuously distributed delays are discussed. By using Brouwer’s fixed point theorem, matrix theory and analysis techniques such as Gronwall inequality, some new sufficient conditions guaranteeing the existence, uniqueness of an equilibrium point and its global asymptotic stability are obtained. An example is given to illustrate the theoretical results.

MSC:
93D20Asymptotic stability of control systems
34K35Functional-differential equations connected with control problems
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References:
[1] Arik, S.: IEEE trans. Neural networks. 13, No. 5, 1239 (2002)
[2] Arik, S.: IEEE trans. Circuits systems I. 49, No. 8, 1211 (2002)
[3] Arik, S.: IEEE trans. Circuits systems I. 50, No. 1, 156 (2003)
[4] Bélair, J.: J. dynamics differential equations. 5, 607 (1993)
[5] Cao, J.: IEEE trans. Circuits systems I. 48, No. 11, 1330 (2001)
[6] Cao, J.: Phys. lett. A. 307, 136 (2003)
[7] Cao, J.; Wang, J.: IEEE trans. Circuits systems I. 50, No. 1, 34 (2003)
[8] Chen, T.; Amari, S.: IEEE trans. Neural networks. 12, No. 1, 159 (2001)
[9] Chen, T.: Neural networks. 14, 251 (2001) · Zbl 0992.34059
[10] Chen, Y.: Neural networks. 15, 867 (2002) · Zbl 1123.68342
[11] Cohen, M.; Grossberg, S.: IEEE trans. Systems man cybernet.. 13, 815 (1983)
[12] Den Driessche, P. Van; Zou, X.: SIAM J. Appl. math.. 58, 1878 (1998)
[13] Gopalsamy, K.: Stability and oscillations in delay differential equations of population dynamics. (1992) · Zbl 0752.34039
[14] Gopalsamy, K.; He, X.: Physica D. 76, 344 (1994)
[15] Horn, R. A.; Johnson, C. R.: Matrix analysis. (1990) · Zbl 0704.15002
[16] Hopfield, J. J.: Proc. natl. Acad. sci. USA. 79, 2254 (1982)
[17] Hopfield, J. J.: Proc. natl. Acad. sci. USA. 81, 3088 (1984)
[18] Hopfield, J. J.; Tank, D. W.: Science. 233, 3088 (1986)
[19] Liao, X.: Absolute stability of nonlinear control systems. (1993) · Zbl 0817.93002
[20] Mohamad, S.; Gopalsamy, K.: Math. comput. Simulation. 53, 1 (2000)
[21] Marcus, C.; Westervelt, R.: Phys. rev. A. 39, 347 (1989)
[22] Quezz, A.; Protoposecu, V.; Barben, J.: IEEE trans. Systems man cybernet.. 18, 80 (1983)
[23] Rao, V. Sree Hari; Phaneendra, B. R. M.: Neural networks. 12, 445 (1999)
[24] Wu, J.: Trans. amer. Math. soc.. 350, 4799 (1999)
[25] Wang, L.; Zou, X. F.: Neural networks. 15, 415 (2002) · Zbl 1025.92002
[26] Wang, L.; Zou, X. F.: Physica D. 170, 162 (2002)
[27] Ye, H.; Michel, A. N.; Wang, K.: Phys. rev. E. 51, 2611 (1995)
[28] Zhang, Y.; Heng, A.; Vadakkepat, P.: IEEE trans. Circuits systems I. 49, No. 2, 256 (2002)
[29] Zhang, J.; Jin, X.: Neural networks. 13, 745 (2000)
[30] Zhang, Q.; Ma, R.; Xu, J.: Commun. theor. Phys.. 39, 381 (2003)
[31] Zhao, H.: Phys. lett. A. 297, 182 (2002)
[32] Zhao, H.: Neural networks. 17, 47 (2004) · Zbl 1058.35113