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Input-to-state stability of impulsive reaction–diffusion neural networks with infinite distributed delays

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Abstract

In this paper, we focus on the global existence–uniqueness and input-to-state stability of the mild solution of impulsive reaction–diffusion neural networks with infinite distributed delays. First, the model of the impulsive reaction–diffusion neural networks with infinite distributed delays is reformulated in terms of an abstract impulsive functional differential equation in Hilbert space and the local existence–uniqueness of the mild solution on impulsive time interval is proven by the Picard sequence and semigroup theory. Then, the diffusion–dependent conditions for the global existence–uniqueness and input-to-state stability are established by the vector Lyapunov function and M-matrix where the infinite distributed delays are handled by a novel vector inequality. It shows that the ISS properties can be retained for the destabilizing impulses if there are no too short intervals between the impulses. Finally, three numerical examples verify the effectiveness of the theoretical results and that the reaction–diffusion benefits the input-to-state stability of the neural-network system.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    Tengda Wei & Xiaodi Li

  2. Department of Automatic Control, Robotics and Fluid Technique, Faculty of Mechanical and Civil Engineering, University of Kragujevac, Dositejeva 19, 36000, Kraljevo, Serbia

    Vladimir Stojanovic

Authors
  1. Tengda Wei
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  2. Xiaodi Li
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  3. Vladimir Stojanovic
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Correspondence to Tengda Wei.

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This work was supported by the National Natural Science Foundation of China (61673247, 11771014), the Research Fund for Excellent Youth Scholars of Shandong Province (JQ201719), the China Postdoctoral Science Foundation (2020M672109), the Shandong Province Postdoctoral Innovation Project, and the Serbian Ministry of Education, Science and Technological Development (No. 451-03-68/2020-14/200108).

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Wei, T., Li, X. & Stojanovic, V. Input-to-state stability of impulsive reaction–diffusion neural networks with infinite distributed delays. Nonlinear Dyn 103, 1733–1755 (2021). https://doi.org/10.1007/s11071-021-06208-6

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  • DOI: https://doi.org/10.1007/s11071-021-06208-6

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