Exponential stability of periodic solutions of recurrent neural networks with functional dependence on piecewise constant argument

AKHMET M., ARUĞASLAN ÇİNÇİN D., Cengiz N.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.1, pp.272-292, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1606-138
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.272-292
  • Keywords: Recurrent neural networks, functional differential equations, piecewise constant argument, periodic solution, stability, RETARDED DIFFERENTIAL-EQUATIONS, DELAY
  • Middle East Technical University Affiliated: Yes

Abstract

In this study, we develop a model of recurrent neural networks with functional dependence on piecewise constant argument of generalized type. Using the theoretical results obtained for functional differential equations with piecewise constant argument, we investigate conditions for existence and uniqueness of solutions, bounded solutions, and exponential stability of periodic solutions. We provide conditions based on the parameters of the model.