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Neural Netw. 2015 Aug;68:78-88. doi: 10.1016/j.neunet.2015.04.006. Epub 2015 May 6.

Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks.

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College of Mathematics and Statistics, Hubei Normal University, Hubei Huangshi 435002, China. Electronic address:
School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China; Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China. Electronic address:


We study the global asymptotic ω-periodicity for a fractional-order non-autonomous neural networks. Firstly, based on the Caputo fractional-order derivative it is shown that ω-periodic or autonomous fractional-order neural networks cannot generate exactly ω-periodic signals. Next, by using the contraction mapping principle we discuss the existence and uniqueness of S-asymptotically ω-periodic solution for a class of fractional-order non-autonomous neural networks. Then by using a fractional-order differential and integral inequality technique, we study global Mittag-Leffler stability and global asymptotical periodicity of the fractional-order non-autonomous neural networks, which shows that all paths of the networks, starting from arbitrary points and responding to persistent, nonconstant ω-periodic external inputs, asymptotically converge to the same nonconstant ω-periodic function that may be not a solution.


Fractional-order neural networks; Global asymptotical periodicity; Globally Mittag-Leffler stable; S-asymptotically -periodic solution

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