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Graph-Theoretic Approach to Finite-Time Synchronization for Fuzzy Cohen–Grossberg Neural Networks with Mixed Delays and Discontinuous Activations

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Abstract

This paper investigates finite-time synchronization for fuzzy Cohen–Grossberg neural networks (FCGNNs) with mixed delays and discontinuous activations via state-feedback control. The features of FCGNNs, discrete time delays, distributed delays and discontinuous activations are taken into account which makes our networks more general and practical in comparison with the most existing Cohen–Grossberg neural networks. Two switching state-feedback controllers designed for the implement of finite-time synchronization can be used to effectively overcome the limitations of the traditional continuous linear feedback controllers. Different from previous work, graph theory and Lyapunov method are used to study finite-time synchronization of FCGNNs for the first time in this paper, then some sufficient criteria are obtained to guarantee the finite-time synchronization of FCGNNs. In particular, it is worth noting that the settling time for finite-time synchronization is closely related to the topological structure of FCNNs. Finally, two numerical examples are given to verify the feasibility and effectiveness of the theoretical results.

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Funding

This work is supported by the Fundamental Research Funds for the Central Universities (No. 2572016CB08).

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Authors and Affiliations

  1. Department of Mathematics, Northeast Forestry University, Harbin, 150040, Heilongjiang, PR China

    Dongsheng Xu & Ming Liu

  2. Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, 264209, PR China

    Chengqiang Xu

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  1. Dongsheng Xu
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  2. Chengqiang Xu
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  3. Ming Liu
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Correspondence to Ming Liu.

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Appendix

Appendix

The values of elements in matrixes \((\alpha _{kh})_{20\times 20}\), \((\beta _{kh})_{20\times 20}\), \((H_{kh})_{20\times 20}\) and \((T_{kh})_{20\times 20}\) are shown as follows, while the elements unmentioned are set as 0 (Tables 2, 3):

Table 2 The elements in the matrix \((\alpha _{kh})_{l\times l}\) and \((\beta _{kh})_{l\times l}\)
Full size table
Table 3 The elements in the matrix \((T_{kh})_{l\times l}\) and \((H_{kh})_{l\times l}\)
Full size table

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Xu, D., Xu, C. & Liu, M. Graph-Theoretic Approach to Finite-Time Synchronization for Fuzzy Cohen–Grossberg Neural Networks with Mixed Delays and Discontinuous Activations. Neural Process Lett 52, 905–933 (2020). https://doi.org/10.1007/s11063-020-10237-4

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