Two-dimensional master stability function analysis of synchronization in periodic and chaotic networks

AIMS Mathematics 2026 Open access

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Authors: Tayebeh Moalemi, Gopinath Barathi, Atiyeh Bayani, Karthikeyan Rajagopal, Sajad Jafari, Matjaž Perc
DOI: 10.3934/math.2026269
Cited by: 0
References: 59

Abstract

Here we used the master stability function (MSF) framework to develop a two-dimensional MSF representation that incorporates both real and complex eigenvalues, thereby capturing the dynamics of diagonalizable directed networks. Our analysis shows how synchronization stability depends on complex coupling strengths and reveals conditions under which bounded or unbounded regions of negative MSF arise, corresponding to stable synchronization. This two-dimensional approach unifies periodic and chaotic dynamics within a common framework, offering sharper insights into when and how diagonalizable directed networks can sustain coherent collective behavior.

Fields of Study & Subjects

Nonlinear Dynamics and Pattern Formation Neural Networks Stability and Synchronization Chaos control and synchronization

Publication details

Journal / source
AIMS Mathematics
Volume
11
Issue
3
Pages
6499–6524
Publication date
1 January 2026
Language
EN