Liu, Bingwen; Huang, Lihong Existence and exponential stability of periodic solutions for a class of Cohen-Grossberg neural networks with time-varying delays. (English) Zbl 1145.34049 Chaos Solitons Fractals 32, No. 2, 617-627 (2007). A class of Cohen-Grossberg neural networks with time-varying delays is studied. Sufficient conditions for existence and exponentially stability of the periodic solutions are obtained by means of the concidence degree theorem and differential inequality techniques. An illustrative example is given as well. Reviewer: Angela Slavova (Sofia) Cited in 11 Documents MSC: 34K60 Qualitative investigation and simulation of models involving functional-differential equations 92B20 Neural networks for/in biological studies, artificial life and related topics 34K20 Stability theory of functional-differential equations 34K13 Periodic solutions to functional-differential equations Keywords:Cohen-Grossberg neural network; periodic solutions; exponential stability; time-varying delays PDFBibTeX XMLCite \textit{B. Liu} and \textit{L. Huang}, Chaos Solitons Fractals 32, No. 2, 617--627 (2007; Zbl 1145.34049) Full Text: DOI References: [1] Cao, J., Global stability analysis in delayed cellular neural networks, Phys Rev E, 59, 5940-5944 (1999) [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] 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 [6] Wang, L.; Zou, X., Harmless delays in Cohen-Grossberg neural networks, Physics 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 Networks, 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 Networks, 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 Networks, 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] LaSalle, J. P., The stability of dynamical system (1976), SIAM: SIAM Philadelphia · Zbl 0364.93002 [17] Gaines, R. E.; Mawhin, J. L., Coincidence degree, and nonlinear differential equations (1977), Springer-Verlag: Springer-Verlag Berlin · Zbl 0326.34021 [18] Phys Lett A, 317, 436-449 (2003) · Zbl 0983.65079 [19] Berman, A.; Plemmons, R. J., Nonnegative matrices in the mathematical science (1979), Academic Press: Academic Press New York 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.