New convergence on inertial neural networks with time-varying delays and continuously distributed delays

Qian Cao; Xin Long; Qian Cao; Xin Long

doi:10.3934/math.2020381

AIMS Mathematics

2020, Volume 5, Issue 6: 5955-5968. doi: 10.3934/math.2020381

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Research article

New convergence on inertial neural networks with time-varying delays and continuously distributed delays

Qian Cao ¹,
Xin Long ^{2
,
,}

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

Received: 22 May 2020 Accepted: 08 July 2020 Published: 21 July 2020
MSC : 34C25, 34K13, 34K25

In this paper, a class of inertial neural networks with bounded time-varying delays and unbounded continuously distributed delays are explored by applying non-reduced order method. Based upon differential inequality techniques and Lyapunov function method, a new sufficient condition is presented to ensure all solutions of the addressed model and their derivatives converge to zero vector, which refines some previously known researches. Moreover, a numerical example is provided to illustrate these analytical conclusions.
- inertial neural networks,
- time-varying delay,
- distributed delay,
- global convergence
Citation: Qian Cao, Xin Long. New convergence on inertial neural networks with time-varying delays and continuously distributed delays[J]. AIMS Mathematics, 2020, 5(6): 5955-5968. doi: 10.3934/math.2020381

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Abstract

In this paper, a class of inertial neural networks with bounded time-varying delays and unbounded continuously distributed delays are explored by applying non-reduced order method. Based upon differential inequality techniques and Lyapunov function method, a new sufficient condition is presented to ensure all solutions of the addressed model and their derivatives converge to zero vector, which refines some previously known researches. Moreover, a numerical example is provided to illustrate these analytical conclusions.

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