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Global Asymptotic Stability of Periodic Solutions for Discrete Time Delayed BAM Neural Networks by Combining Coincidence Degree Theory with LMI Method

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Abstract

In this paper, we are concerned with the existence and global asymptotic stability of periodic solutions for a class of delayed discrete-time BAM neural networks. Instead of using the method of the priori estimate of periodic solutions in existing papers to study periodic solutions of neural networks, by combining Mawhin’s continuation theorem of coincidence degree theory with linear matrix inequality (LMI) method as well as inequality techniques, some novel LMI-based sufficient conditions to guarantee the existence and global asymptotic stability of periodic solutions for the neural networks are established. Our results which are both dependent on time delay and external inputs of the neural networks are new and complementary to the existing papers.

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

    Ling Ren, Xuejun Yi & Zhengqiu Zhang

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  1. Ling Ren
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  2. Xuejun Yi
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  3. Zhengqiu Zhang
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Correspondence to Xuejun Yi.

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Project supported by the Innovation Platform Open Fund in Hunan Province Colleges and Universities of China (No: 201485) and China Hunan Provincial Science and Technology Department (2015JC3050).

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Ren, L., Yi, X. & Zhang, Z. Global Asymptotic Stability of Periodic Solutions for Discrete Time Delayed BAM Neural Networks by Combining Coincidence Degree Theory with LMI Method. Neural Process Lett 50, 1321–1340 (2019). https://doi.org/10.1007/s11063-018-9909-2

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