Exponential stability of periodic solution for stochastic neural networks involving multiple time-varying delays

Zhigang Zhou; Li Wan; Qunjiao Zhang; Hongbo Fu; Huizhen Li; Qinghua Zhou; Zhigang Zhou; Li Wan; Qunjiao Zhang; Hongbo Fu; Huizhen Li; Qinghua Zhou

doi:10.3934/math.2024723

AIMS Mathematics

2024, Volume 9, Issue 6: 14932-14948. doi: 10.3934/math.2024723

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Research article

Exponential stability of periodic solution for stochastic neural networks involving multiple time-varying delays

1.
Research Center of Nonlinear Science, Research Center for Applied Mathematics and Interdisciplinary Sciences, School of Mathematical and Physical Sciences, Wuhan Textile University, Wuhan 430073, China
2.
School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China

Received: 03 March 2024 Revised: 10 April 2024 Accepted: 18 April 2024 Published: 24 April 2024
MSC : 32D40

This paper discusses the exponential stability of periodic solutions for stochastic neural networks with multiple time-varying delays. For these networks, sufficient conditions in the linear matrix inequality forms are rare in the literature. We constructed an appropriate Lyapunov-Krasovskii functional to eliminate the items with multiple delays and establish some sufficient conditions in linear matrix inequality forms, to ensure exponential stability of the periodic solutions. Several examples are provided to demonstrate that our results are effective and less conservative than previous ones.
- stochastic neural network,
- multiple time-varying delays,
- periodic solution,
- exponential stability
Citation: Zhigang Zhou, Li Wan, Qunjiao Zhang, Hongbo Fu, Huizhen Li, Qinghua Zhou. Exponential stability of periodic solution for stochastic neural networks involving multiple time-varying delays[J]. AIMS Mathematics, 2024, 9(6): 14932-14948. doi: 10.3934/math.2024723

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Abstract

This paper discusses the exponential stability of periodic solutions for stochastic neural networks with multiple time-varying delays. For these networks, sufficient conditions in the linear matrix inequality forms are rare in the literature. We constructed an appropriate Lyapunov-Krasovskii functional to eliminate the items with multiple delays and establish some sufficient conditions in linear matrix inequality forms, to ensure exponential stability of the periodic solutions. Several examples are provided to demonstrate that our results are effective and less conservative than previous ones.

References

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