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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


A New Comparison Theorem and Stability Analysis of Fractional Order Cohen-Grossberg Neural Networks

Discontinuity, Nonlinearity, and Complexity 7(1) (2018) 43--53 | DOI:10.5890/DNC.2018.03.004

Xiaolei Liu, Jian Yuan, Gang Zhou, Wenfei Zhao

School of Basic Sciences for Aviation, Naval Aviation University, Yantai 264001, P.R.China

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This paper proposes a new comparison theorem and stability analysis of fractional order Cohen-Grossberg neural networks. Firstly, a new comparison theorem for fractional order systems is proved. Secondly, the stability of a class of fractional order Cohen-Grossberg neural networks with Caputo derivative is investigated on the basis of the above comparison theorem. Thirdly, sufficient conditions of stability of the neural networks are obtained utilizing the property of Mittag-Leffler functions, the generalized Gronwall-Bellman inequality and the method of the integral transform. Furthermore, a numerical simulation example is presented to illustrate the effectiveness of these results.


All the authors acknowledge the valuable suggestions from the peer reviewers. This work was supported by the Natural Science Foundation of Shandong Province (Grant No. ZR2014AM006).


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