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Global Exponential Stability Analysis of Commutative Quaternion-Valued Neural Networks with Time Delays on Time Scales

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Abstract

In order to avoid the non-commutativity multiplication of quaternion, the commutative quaternion-valued neural networks (CQVNNs) with time delays are established on time scales, which can bring two different forms of discrete-time and continuous-time CQVNNs into a single framework. First, CQVNNs will be transformed into two complex-valued neural networks via the multiplication rules of commutative quaternion. Then, different sufficient criteria for global exponential stability of CQVNNs are studied mainly by employing matrix measure and some inequalities on time scales. Finally, two numerical examples will be used to verify the feasibility and validity for the achieved consequences.

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Authors and Affiliations

  1. Department of Mathematics, Chongqing Jiaotong University, Chongqing, 400074, China

    Yannan Xia, Xiaofeng Chen, Bing Li & Xujun Yang

  2. College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China

    Dongyuan Lin

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  1. Yannan Xia
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  2. Xiaofeng Chen
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Correspondence to Xiaofeng Chen.

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This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 62276035 and 61906023), in part by Natural Science Foundation of Chongqing (Grant No. CSTB2022NSCQ- MSX0370), in part by Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJZD-M202100701), in part by Joint Training Base Construction Project for Graduate Students in Chongqing (Grant No. JDLHPYJD2021016), and in part by Group Building Scientific Innovation Project for universities in Chongqing (Grant No. CXQT21021).

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Xia, Y., Chen, X., Lin, D. et al. Global Exponential Stability Analysis of Commutative Quaternion-Valued Neural Networks with Time Delays on Time Scales. Neural Process Lett 55, 6339–6360 (2023). https://doi.org/10.1007/s11063-022-11141-9

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