On the differential equations of recurrent neural networks

Abstract

In this paper, a recurrent neural network with mixed delays which plays an important role is considered. We are concerned with the existence, uniqueness and global exponential stability of the doubly measure pseudo almost automorphic solutions. First, we establish results that are interesting on the functional space of such functions like composition theorem. Second, by employing the fixed-point theorem and some properties of the measure pseudo almost automorphic functions, some sufficient conditions for the existence, uniqueness and global exponential stability of the doubly measure pseudo almost automorphic solutions have been established. Our results obtained in this paper are new. Finally, two commonly used numerical examples are given to illustrate the effectiveness of the obtained results.

Keywords:

• Pseudo almost automorphic
• double measure
• recurrent neural networks
• mixed delays

2010 Mathematics Subject Classifications:

• 34C27
• 34K14
• 35B15
• 37B25
• 92C20

Disclosure statement

The authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.