Asymptotic stability for quaternion-valued BAM neural networks via a contradictory method and two Lyapunov functionals

Ailing Li; Mengting Lv; Yifang Yan; Ailing Li; Mengting Lv; Yifang Yan

doi:10.3934/math.2022457

AIMS Mathematics

2022, Volume 7, Issue 5: 8206-8223. doi: 10.3934/math.2022457

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Research article

Asymptotic stability for quaternion-valued BAM neural networks via a contradictory method and two Lyapunov functionals

1.
College of Science, Hebei North University, Zhangjiakou, 075000, China
2.
School of Mathematics, Hunan University, Changsha, 410082, China

Received: 10 December 2021 Revised: 11 February 2022 Accepted: 14 February 2022 Published: 25 February 2022
MSC : 34K24

We explore the existence and asymptotic stability of equilibrium point for a class of quaternion-valued BAM neural networks with time-varying delays. Firstly, by employing Homeomorphism theorem and a contradictory method with novel analysis skills, a criterion ensuring the existence of equilibrium point of the considered quaternion-valued BAM neural networks is acquired. Secondly, by constructing two Lyapunov functionals, a criterion assuring the global asymptotic stability of equilibrium point for above discussed quaternion-valued BAM is presented. Applying a contradictory method to study the equilibrium point and applying two Lyapunov functionals to study stability of equilibrium point are completely new methods.
- quaternion-valued BAM neural networks,
- contradictory method,
- asymptotic stability,
- Lyapunov functionals
Citation: Ailing Li, Mengting Lv, Yifang Yan. Asymptotic stability for quaternion-valued BAM neural networks via a contradictory method and two Lyapunov functionals[J]. AIMS Mathematics, 2022, 7(5): 8206-8223. doi: 10.3934/math.2022457

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Abstract

We explore the existence and asymptotic stability of equilibrium point for a class of quaternion-valued BAM neural networks with time-varying delays. Firstly, by employing Homeomorphism theorem and a contradictory method with novel analysis skills, a criterion ensuring the existence of equilibrium point of the considered quaternion-valued BAM neural networks is acquired. Secondly, by constructing two Lyapunov functionals, a criterion assuring the global asymptotic stability of equilibrium point for above discussed quaternion-valued BAM is presented. Applying a contradictory method to study the equilibrium point and applying two Lyapunov functionals to study stability of equilibrium point are completely new methods.

References

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