Finite-time stabilization in probability for stochastic reaction–diffusion Cohen–Grossberg neural networks with mixed delays

Yue Yu; Yue Yu

doi:10.3934/era.2026200

Electronic Research Archive

2026, Volume 34, Issue 7: 4535-4559. doi: 10.3934/era.2026200

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Research article

Finite-time stabilization in probability for stochastic reaction–diffusion Cohen–Grossberg neural networks with mixed delays

Yue Yu ^,

MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China

Received: 26 February 2026 Revised: 13 April 2026 Accepted: 27 April 2026 Published: 26 May 2026

We studied finite-time stabilization in probability for stochastic reaction-diffusion Cohen-Grossberg neural networks with mixed delays and multiplicative noise under Neumann boundary conditions. By developing a Lyapunov-Krasovskii functional and using stochastic theory with the Neumann-Poincaré inequality, we obtained several verifiable stabilization criteria. A componentwise controller with a nonlinear finite-time term was further designed to induce a constant drift effect in the Lyapunov evolution, leading to an explicit stochastic settling time bound that quantifies the roles of diffusion, delays, couplings, noise, and control gains. Simulations confirmed the effectiveness of the proposed method.
- finite-time stabilization,
- stochastic reaction-diffusion,
- mixed delays,
- generalized Halanay inequality,
- Lyapunov-Krasovskii functional
Citation: Yue Yu. Finite-time stabilization in probability for stochastic reaction–diffusion Cohen–Grossberg neural networks with mixed delays[J]. Electronic Research Archive, 2026, 34(7): 4535-4559. doi: 10.3934/era.2026200

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Abstract

We studied finite-time stabilization in probability for stochastic reaction-diffusion Cohen-Grossberg neural networks with mixed delays and multiplicative noise under Neumann boundary conditions. By developing a Lyapunov-Krasovskii functional and using stochastic theory with the Neumann-Poincaré inequality, we obtained several verifiable stabilization criteria. A componentwise controller with a nonlinear finite-time term was further designed to induce a constant drift effect in the Lyapunov evolution, leading to an explicit stochastic settling time bound that quantifies the roles of diffusion, delays, couplings, noise, and control gains. Simulations confirmed the effectiveness of the proposed method.

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