Stabilization of stochastic coopetition neural networks with time-varying delays in the space-time discretised frame

Ting Yuan and Tianwei Zhang

International Journal of Systems Science, 2025, vol. 56, issue 16, 3999-4015

Abstract: By the aid of the time Euler difference and the finite difference, this paper discusses the realm of global stabilisations in the mean-squared sense of space-time discrete stochastic coopetition neural networks with time-varying delays and Dirichlet, Neumann boundaries. It presents some criteria of global asymptotic stabilisation in the mean-squared sense for stochastic coopetition neural networks through the methods of the Lyapunov-Krasovskii function and the discrete Wirtinger inequality. The current research considers global exponential stabilisation in the mean-squared sense, which offers a more comprehensive view of stabilised networks than asymptotic stabilisation. By transforming the left Dirichlet boundary into Reumann boundary, the researchers also discuss global stabilisations in the mean-squared sense of space-time discrete networks. More importantly, this study shows that it can achieve better global mean-squared stabilisations of space-time discrete networks endowed with the smaller diffusion intensities, smaller coupling strengths and bigger connection weights. In comparison to preceding researches in this area, this paper presents a framework for discussing issues of global stabilisation in the context of space-time discrete networks. Furthermore, the article concludes with an illustrative example that demonstrates the effectiveness of the proposed methodology.

Date: 2025
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DOI: 10.1080/00207721.2025.2481997

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