Existence, Uniqueness and Exponential Stability of Periodic Solution for Discrete-Time Delayed BAM Neural Networks Based on Coincidence Degree Theory and Graph Theoretic Method

• Main Authors: Manickam Iswarya, Ramachandran Raja, Grienggrai Rajchakit, Jinde Cao, Jehad Alzabut, Chuangxia Huang
• Format: Article
• Language: English
• Published: MDPI AG 2019-11-01
• Series: Mathematics
• Subjects: discrete-time bamnns; periodic solution; coincidence degree theory; exponential stability; krichhoff’s matrix tree theorem; time-varying delays
• Online Access: https://www.mdpi.com/2227-7390/7/11/1055
• ISSN: 2227-7390

In this work, a general class of discrete time bidirectional associative memory (BAM) neural networks (NNs) is investigated. In this model, discrete and continuously distributed time delays are taken into account. By utilizing this novel method, which incorporates the approach of Kirchhoff’s matrix tree theorem in graph theory, Continuation theorem in coincidence degree theory and Lyapunov function, we derive a few sufficient conditions to ensure the existence, uniqueness and exponential stability of the periodic solution of the considered model. At the end of this work, we give a numerical simulation that shows the effectiveness of this work.