Exponential stability of stochastic Hopfield neural network with mixed multiple delays

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

doi:10.3934/math.2021245

AIMS Mathematics

2021, Volume 6, Issue 4: 4142-4155. doi: 10.3934/math.2021245

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Research article

Exponential stability of stochastic Hopfield neural network with mixed multiple delays

1.
School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, 266061, PR China
2.
School of Mathematics and Computer Science, Engineering Research Center of Hubei Province for Clothing Information, Research Centre of Nonlinear Science, Wuhan Textile University, Wuhan, 430073, PR China

Received: 24 December 2020 Accepted: 29 January 2021 Published: 05 February 2021
MSC : 34D20

This paper investigates the problem for exponential stability of stochastic Hopfield neural networks involving multiple discrete time-varying delays and multiple distributed time-varying delays. The exponential stability of such neural systems has not been given much attention in the past literature because this type of neural systems cannot be transformed into the vector forms and it is difficult to derive the easily verified stability conditions expressed in terms of the linear matrix inequality. Therefore, this paper tries to establish the easily verified sufficient conditions of the linear matrix inequality forms to ensure the mean-square exponential stability and the almost sure exponential stability for this type of neural systems by constructing a suitable Lyapunov-Krasovskii functional and inequality techniques. Four examples are provided to demonstrate the effectiveness of the proposed theoretical results and compare the established stability conditions to the previous results.
- stochastic Hopfield neural network,
- multiple time-varying delays,
- exponential stability
Citation: Qinghua Zhou, Li Wan, Hongbo Fu, Qunjiao Zhang. Exponential stability of stochastic Hopfield neural network with mixed multiple delays[J]. AIMS Mathematics, 2021, 6(4): 4142-4155. doi: 10.3934/math.2021245

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Abstract

This paper investigates the problem for exponential stability of stochastic Hopfield neural networks involving multiple discrete time-varying delays and multiple distributed time-varying delays. The exponential stability of such neural systems has not been given much attention in the past literature because this type of neural systems cannot be transformed into the vector forms and it is difficult to derive the easily verified stability conditions expressed in terms of the linear matrix inequality. Therefore, this paper tries to establish the easily verified sufficient conditions of the linear matrix inequality forms to ensure the mean-square exponential stability and the almost sure exponential stability for this type of neural systems by constructing a suitable Lyapunov-Krasovskii functional and inequality techniques. Four examples are provided to demonstrate the effectiveness of the proposed theoretical results and compare the established stability conditions to the previous results.

References

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