Anti-periodic dynamics on high-order inertial Hopfield neural networks involving time-varying delays

Qian Cao; Xiaojin Guo; Qian Cao; Xiaojin Guo

doi:10.3934/math.2020347

AIMS Mathematics

2020, Volume 5, Issue 6: 5402-5421. doi: 10.3934/math.2020347

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Research article

Anti-periodic dynamics on high-order inertial Hopfield neural networks involving time-varying delays

Qian Cao ¹,
Xiaojin Guo ^{2
,
,}

1.
College of Mathematics and Physics, Hunan University of Arts and Science, Changde, Hunan 415000, P. R. China
2.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, 410114, China

Received: 17 April 2020 Accepted: 12 June 2020 Published: 23 June 2020
MSC : 34C25, 34K13, 34K25

Taking into accounting time-varying delays and anti-periodic environments, this paper deals with the global convergence dynamics on a class of anti-periodic high-order inertial Hopfield neural networks. First of all, with the help of Lyapunov function method, we prove that the global solutions are exponentially attractive to each other. Secondly, by using analytical techniques in uniform convergence functions sequence, the existence of the anti-periodic solution and its global exponential stability are established. Finally, two examples are arranged to illustrate the effectiveness and feasibility of the obtained results.
- high-order inertial neural networks,
- anti-periodic solution,
- global exponential stability,
- time-varying delay
Citation: Qian Cao, Xiaojin Guo. Anti-periodic dynamics on high-order inertial Hopfield neural networks involving time-varying delays[J]. AIMS Mathematics, 2020, 5(6): 5402-5421. doi: 10.3934/math.2020347

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Abstract

Taking into accounting time-varying delays and anti-periodic environments, this paper deals with the global convergence dynamics on a class of anti-periodic high-order inertial Hopfield neural networks. First of all, with the help of Lyapunov function method, we prove that the global solutions are exponentially attractive to each other. Secondly, by using analytical techniques in uniform convergence functions sequence, the existence of the anti-periodic solution and its global exponential stability are established. Finally, two examples are arranged to illustrate the effectiveness and feasibility of the obtained results.

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