Anti-periodic synchronization of quaternion-valued high-order Hopfield neural networks with delays

Jin Gao; Lihua Dai; Jin Gao; Lihua Dai

doi:10.3934/math.2022775

AIMS Mathematics

2022, Volume 7, Issue 8: 14051-14075. doi: 10.3934/math.2022775

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Research article

Anti-periodic synchronization of quaternion-valued high-order Hopfield neural networks with delays

Jin Gao ^{1
,
,},
Lihua Dai ²

1.
School of Information, Yunnan Communications Vocational and Technical College, Kunming, Yunnan 650500, China
2.
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received: 24 March 2022 Revised: 05 May 2022 Accepted: 20 May 2022 Published: 27 May 2022
MSC : 34D06, 34D23, 34K13, 34K24

This paper proposes a class of quaternion-valued high-order Hopfield neural networks with delays. By using the non-decomposition method, non-reduced order method, analytical techniques in uniform convergence functions sequence, and constructing Lyapunov function, we obtain several sufficient conditions for the existence and global exponential synchronization of anti-periodic solutions for delayed quaternion-valued high-order Hopfield neural networks. Finally, an example and its numerical simulations are given to support the proposed approach. Our results play an important role in designing inertial neural networks.
- inertial neural networks,
- quaternion,
- anti-periodic solutions,
- non-reduced order method,
- synchronization
Citation: Jin Gao, Lihua Dai. Anti-periodic synchronization of quaternion-valued high-order Hopfield neural networks with delays[J]. AIMS Mathematics, 2022, 7(8): 14051-14075. doi: 10.3934/math.2022775

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Abstract

This paper proposes a class of quaternion-valued high-order Hopfield neural networks with delays. By using the non-decomposition method, non-reduced order method, analytical techniques in uniform convergence functions sequence, and constructing Lyapunov function, we obtain several sufficient conditions for the existence and global exponential synchronization of anti-periodic solutions for delayed quaternion-valued high-order Hopfield neural networks. Finally, an example and its numerical simulations are given to support the proposed approach. Our results play an important role in designing inertial neural networks.

References

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