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

Manickam Iswarya, Ramachandran Raja, Grienggrai Rajchakit, Jinde Cao, Jehad Alzabut and Chuangxia Huang
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Manickam Iswarya: Department of Mathematics, Alagappa University, Karaikudi 630 004, India
Ramachandran Raja: Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630 004, India
Grienggrai Rajchakit: Department of Mathematics, Maejo University, Chiangmai 50290, Thailand
Jinde Cao: School of Mathematics, Southeast University, Nanjing 211189, China
Jehad Alzabut: Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Chuangxia Huang: Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Department of Applied Mathematics, Changsha University of Science and Technology, Changsha 410114, China

Mathematics, 2019, vol. 7, issue 11, 1-18

Abstract: 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.

Keywords: discrete-time BAMNNs; periodic solution; coincidence degree theory; exponential stability; Krichhoff’s matrix tree theorem; time-varying delays (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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