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

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Department of Mathematics, Alagappa University, Karaikudi 630 004, India
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Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630 004, India
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Department of Mathematics, Maejo University, Chiangmai 50290, Thailand
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School of Mathematics, Southeast University, Nanjing 211189, China
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Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
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Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Department of Applied Mathematics, Changsha University of Science and Technology, Changsha 410114, China
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Authors to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1055; https://doi.org/10.3390/math7111055
Received: 25 August 2019 / Revised: 17 October 2019 / Accepted: 24 October 2019 / Published: 4 November 2019
(This article belongs to the Special Issue Impulsive Control Systems and Complexity)
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. View Full-Text
Keywords: discrete-time BAMNNs; periodic solution; coincidence degree theory; exponential stability; Krichhoff’s matrix tree theorem; time-varying delays discrete-time BAMNNs; periodic solution; coincidence degree theory; exponential stability; Krichhoff’s matrix tree theorem; time-varying delays
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MDPI and ACS Style

Iswarya, M.; Raja, R.; Rajchakit, G.; Cao, J.; Alzabut, J.; Huang, C. Existence, Uniqueness and Exponential Stability of Periodic Solution for Discrete-Time Delayed BAM Neural Networks Based on Coincidence Degree Theory and Graph Theoretic Method. Mathematics 2019, 7, 1055.

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