Abstract
In this paper, we study the global exponential stability of anti-periodic solution of Cohen-Grossberg neural networks with mixed delays and distributed delays. Based on Lyapunov function and contraction map** theorem, we introduce some sufficient conditions to ensure the existence and exponential stability of anti-periodic solution of Cohen-Grossberg neural networks. Finally, some numerical examples are provided to show the effectiveness of the obtained results.
W. Fuqiang—This research is supported by the national science fund of grant (61403101), and Weihai Science and technology Development Plan Project (2014DXGJ07).
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References
Abdurahman, A., Jiang, H.: The existence and stability of the anti-periodic solution for delayed Cohen-Grossberg neural networks with impulsive effects. Neurocomputing 149, 22–28 (2015)
Bai, C.: Global exponential stability and existence of periodic solution of Cohen-Grossberg type neural networks with delays and impulses. Nonlinear Anal. Real World Appl. 9, 747–761 (2008)
Chen, H.: Antiperiodic wavelets. J. Comput. Math. Int. Ed. 14, 32–39 (1996)
Chen, X., Song, Q.: Global exponential stability of the periodic solution of delayed Cohen-Grossberg neural networks with discontinuous activations. Neurocomputing 73, 3097–3104 (2010)
Cohen, M., Grossberg, S., et al.: Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. 5, 815–826 (1983)
Delvos, F.J., Knoche, L.: Lacunary interpolation by antiperiodic trigonometric polynomials. BIT Numer. Math. 39, 439–450 (1999)
Gong, S.: Anti-periodic solutions for a class of Cohen-Grossberg neural networks. Comput. Math. Appl. 58, 341–347 (2009)
Li, B., Xu, D.: Existence and exponential stability of periodic solution for impulsive Cohen-Grossberg neural networks with time-varying delays. Appl. Math. Comput. 219, 2506–2520 (2012)
Li, G., Sun, C.: Global stability of Cohen-Grossberg neural network with time-varying delays via nonlinear measure. J. Comput. Inf. Syst. 9, 1389–1398 (2013)
Li, X.: Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type bam neural networks with continuously distributed delays. Appl. Math. Comput. 215, 292–307 (2009)
Li, Y., Yang, L.: Anti-periodic solutions for Cohen-Grossberg neural networks with bounded and unbounded delays. Commun. Nonlinear Sci. Numer. Simul. 14, 3134–3140 (2009)
Song, Q., Zhang, J.: Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays. Nonlinear Anal. Real World Appl. 9, 500–510 (2008)
Wang, D., Huang, L.: Periodicity and global exponential stability of generalized Cohen-Grossberg neural networks with discontinuous activations and mixed delays. Neural Netw. 51, 80–95 (2014)
Zheng, C.D., Shan, Q.H., Wang, Z.: Novel stability criteria of Cohen-Grossberg neural networks with time-varying delays. Int. J. Circuit Theory Appl. 40, 221–235 (2012)
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Qin, S., Tan, Y., Wang, F. (2016). Exponential Stability of Anti-periodic Solution of Cohen-Grossberg Neural Networks with Mixed Delays. In: Cheng, L., Liu, Q., Ronzhin, A. (eds) Advances in Neural Networks – ISNN 2016. ISNN 2016. Lecture Notes in Computer Science(), vol 9719. Springer, Cham. https://doi.org/10.1007/978-3-319-40663-3_19
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DOI: https://doi.org/10.1007/978-3-319-40663-3_19
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