2007
DOI: 10.1016/j.chaos.2005.11.009
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Existence and exponential stability of periodic solutions for a class of Cohen–Grossberg neural networks with time-varying delays

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Cited by 37 publications
(11 citation statements)
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“…Yuan et al [8] considered existence and global exponential stability of periodic solutions for Cohen-Grossberg neural networks with delays, also using the continuation theorem and Lyapunov function techniques. Liu and Huang [9] considered a class of CohenGrossberg neural networks with time-varying delays without assuming the boundedness, monotonicity, and differentiability of activation functions or any symmetry of interconnections, and established the existence and exponential stability of the periodic solutions. In practice, however, almost periodic oscillation is more general.…”
Section: Introductionmentioning
confidence: 99%
“…Yuan et al [8] considered existence and global exponential stability of periodic solutions for Cohen-Grossberg neural networks with delays, also using the continuation theorem and Lyapunov function techniques. Liu and Huang [9] considered a class of CohenGrossberg neural networks with time-varying delays without assuming the boundedness, monotonicity, and differentiability of activation functions or any symmetry of interconnections, and established the existence and exponential stability of the periodic solutions. In practice, however, almost periodic oscillation is more general.…”
Section: Introductionmentioning
confidence: 99%
“…For example, Fan and Shao (2010) investigated the positive almost periodic solutions for shunting inhibitory cellular neural networks with time-varying and continuously distributed delays, Li and Wang (2012) analyzed the existence and exponential stability of the almost periodic solutions of shunting inhibitory cellular neural networks on time scales, Xia et al (2007) established the sufficient conditions for the existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses, Li and Shu (2011) addressed the existence and exponential stability of antiperiodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales. For more related work on shunting inhibitory cellular neural networks, one can see (Lakshmikantham et al, 1989;Bouzerdoum and Pinter, 1993;Samoilenko and Perestyuk, 1995;Guan and Chen, 1999;Akhmet, 2003;Gopalsamy, 2004;Xu and Yang, 2005;Liu and Huang, 2007;Liu and You, 2007;Xia et al, 2007;Yang and Cao, 2007;Zhang and Li, 2007;Cai et al, 2008;Chen and Zhao, 2008;Li and Wang, 2008;Ou, 2008;Shao, 2008;Xiao and Meng, 2009;Zhou, 2009;Zhang and Gui, 2009;Huang et al, 2010;Shi and Dong, 2010;Peng and Wang, 2013;Peng and Wang, 2013;Zhang, 2013;Wang et al, 2014;Li et al, 0000). studied the existence and stability of almost periodic solutions for the following SICNNs with neutral type delays: where i ¼ 1, 2, .…”
Section: Introductionmentioning
confidence: 99%
“…Mathematical models for artificial neural networks have been established. Neural networks, which are described as continuous differential dynamical systems, have been discussed, and there are extensive results about their dynamical behaviors including equilibriums, periodic solutions, anti-periodic solutions and their respective stability ( [1], [2], [3], [4], [6], [10], [11]). But, in artificial networks for signal and image processing, the finites switching speed of amplifiers may cause delays in the transmission of signals, in addition, faulty elements may experience abrupt changes of state voltage and therefore the normal transient behaviors in processing signal and information are influenced.…”
Section: Introductionmentioning
confidence: 99%