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Stability and Hopf Bifurcation Analysis of a General Tri-diagonal BAM Neural Network with Delays

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Abstract

In this article, a general tri-diagonal bidirectional associative memory (BAM) neural network model with 2n-neurons is proposed. Our investigates have some distinct superiorities, including forward transmission delay and feedback delay in the model are considered. Moreover, the neural network model considered with 2n-neurons is more general in application. We obtain the general expression of characteristic equation of BAM neural network model with 2n-neurons for investigating its stability and Hopf bifurcation. The distribution characteristics of roots of characteristic equation are discussed in detail to get the sufficient conditions for Hopf bifurcation of system caused by delays. Then the designed protocol is simpler and easier to implement compared with some previously investigates. Subsequently, by using the normal form method and central manifold theorem, the direction of Hopf bifurcation and the period and stability of bifurcation periodic solution are determined. Finally, several examples are also utilized to illustrate the validity of theoretical results.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 61374011), and Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2020MF080, ZR2020MF065).

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Authors and Affiliations

  1. School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, 266061, China

    Tianshun Wang, Yu Wang & Zunshui Cheng

  2. School of Mathematics, Southeast University, Nanjing, 211189, China

    Yu Wang

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  1. Tianshun Wang
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  2. Yu Wang
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  3. Zunshui Cheng
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Correspondence to Zunshui Cheng.

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Wang, T., Wang, Y. & Cheng, Z. Stability and Hopf Bifurcation Analysis of a General Tri-diagonal BAM Neural Network with Delays. Neural Process Lett 53, 4571–4592 (2021). https://doi.org/10.1007/s11063-021-10613-8

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