Advanced Mathematical Models & Applications

ISSN Online: 2519-4445

Advanced Mathematical Models & Applications is a peer-reviewed, open access journal meant to publish original and significant results and articles in all areas of mathematical modeling and their applications. The aim of this Journal is to bring together researchers and practitioners from academia and industry to establishing new collaborations in this area. The Journal will consider for publication also review articles, literature reviews, correspondence concerning views and information published in previous issues.

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Sufficient Conditions for Identical Synchronization in a Full Network of n Ordinary Differential Systems of Fitzhugh-Nagumo Type With Linear Coupling and Timedependent External Electrical Stimulation

Phan Van Long Em

Published: 03-12-2025

https://doi.org/10.62476/amma.103473

Abstract

This paper explores the sufficient conditions necessary for achieving identical synchronization in a full network of n interacting ordinary differential systems of Fitz-Hugh-Nagumo type. These systems are characterized by linear coupling and time-dependent external electrical stimulation. The sufficient conditions are established through the construction of an appropriate Lyapunov function. Additionally, this study utilizes R programming to present numerical results that validate the theoretical findings. In this study, we focus exclusively on identical synchronization. Identical synchronization occurs when the dynamic systems within a network exhibit the same properties and patterns at a specific moment in time. In simpler terms, if a network consists of two dynamic equations, synchronization means that one system will replicate the properties and shape of the other system starting from a particular point. When this happens, the network is considered to be in synchronization.