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Neural Computing and Applications

, Volume 31, Issue 11, pp 6933–6943 | Cite as

Positive solutions and exponential stability of positive equilibrium of inertial neural networks with multiple time-varying delays

  • Le Van HienEmail author
  • Le Dao Hai-An
Original Article
  • 140 Downloads

Abstract

This paper is concerned with positive solutions and global exponential stability of positive equilibrium of inertial neural networks with multiple time-varying delays. By utilizing the comparison principle via differential inequalities, we first explore conditions on damping coefficients and self-excitation coefficients to ensure that, with nonnegative connection weights and inputs, all state trajectories of the system initiating in an admissible set of initial conditions are always nonnegative. Then, based on the method of using homeomorphisms, we derive conditions in terms of linear programming problems via M-matrices for the existence, uniqueness, and global exponential stability of a positive equilibrium of the system. Two examples with numerical simulations are given to illustrate the effectiveness of the obtained results.

Keywords

Inertial neural networks Positive equilibrium Exponential stability Time-varying delay 

Notes

Compliance with ethical standards

Conflicts of interest

The authors declare that no potential conflict of interest to be reported to this work.

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Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  1. 1.Department of MathematicsHanoi National University of EducationHanoiVietnam
  2. 2.Department of MathematicsVietnam Maritime UniversityHai PhongVietnam

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