Generalized exponential stability of stochastic Hopfield neural networks with variable coefficients and infinite delay

Dehao Ruan; Yao Lu; Dehao Ruan; Yao Lu

doi:10.3934/math.20241114

AIMS Mathematics

2024, Volume 9, Issue 8: 22910-22926. doi: 10.3934/math.20241114

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Generalized exponential stability of stochastic Hopfield neural networks with variable coefficients and infinite delay

Dehao Ruan ,
Yao Lu ^,

School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China

Received: 18 June 2024 Revised: 18 July 2024 Accepted: 19 July 2024 Published: 25 July 2024
MSC : 34K50, 90B15, 93D20

This paper centers on stochastic Hopfield neural networks with variable coefficients and infinite delay. First, we propose an integral inequality that improves and extends some existing works. Second, by employing some inequalities and stochastic analysis techniques, some sufficient conditions for ensuring $ p $th moment generalized exponential stability are established. Our results do not necessitate the construction of a complex Lyapunov function or rely on the assumption of bounded variable coefficients, and our results expand some existing works. At last, to illustrate the efficacy of our result, we present several simulation examples.
- generalized exponential stability,
- stochastic Hopfield neural networks,
- variable coefficients,
- infinite delay,
- integral inequalities
Citation: Dehao Ruan, Yao Lu. Generalized exponential stability of stochastic Hopfield neural networks with variable coefficients and infinite delay[J]. AIMS Mathematics, 2024, 9(8): 22910-22926. doi: 10.3934/math.20241114

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Abstract

This paper centers on stochastic Hopfield neural networks with variable coefficients and infinite delay. First, we propose an integral inequality that improves and extends some existing works. Second, by employing some inequalities and stochastic analysis techniques, some sufficient conditions for ensuring $ p $th moment generalized exponential stability are established. Our results do not necessitate the construction of a complex Lyapunov function or rely on the assumption of bounded variable coefficients, and our results expand some existing works. At last, to illustrate the efficacy of our result, we present several simulation examples.

References

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