Abstract
In a very recent paper, Peng and Liu (Neural Comput Appl 20:543–547, 2011) investigated the pth moment stability of the stochastic Grossberg–Hopfield neural networks with Markov volatilities by Mao et al. (Bernoulli 6:73–90, 2000, Theorem 4.1). We should point out that Mao et al. (Bernoulli 6:73–90, 2000, Theorem 4.1) investigated the pth moment exponentially stable for a class of stochastic dynamical systems with constant delay; however, this theorem cannot apply to the case of variable time delays. It is also worthy to emphasize that Peng and Liu (Neural Comput Appl 20:543–547, 2011) discussed by Mao et al. (Bernoulli 6:73–90, 2000, Theorem 4.1) the pth moment exponentially stable for the Grossberg–Hopfield neural networks with variable delays, and therefore, there are some gaps between Peng and Liu (Neural Comput Appl 20:543–547, 2011, Theorem 1) and Mao et al. (Bernoulli 6:73–90, 2000, Theorem 4.1). In this paper, we fill up this gap. Moreover, a numerical example is also provided to demonstrate the effectiveness and applicability of the theoretical results.
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Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grants no. 11101054, 11272067, Hunan Provincial Natural Science Foundation of China under Grant no. 12JJ4005 and the Scientific Research Funds of Hunan Provincial Science and Technology Department of China under Grants no. 2012SK3096. Humanities and Social Sciences Foundation of Ministry of Education of China, under Grants no.12YJAZH173.
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Zhu, E., Yang, G. & Liu, J. Comments and further improvements on “pth moment stability of stochastic neural networks with Markov volatilities”. Neural Comput & Applic 23, 1179–1183 (2013). https://doi.org/10.1007/s00521-013-1396-9
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DOI: https://doi.org/10.1007/s00521-013-1396-9