Composed solutions of synchronized patterns in multiplex networks of Kuramoto oscillators

Priya B Jain; Tung T Nguyen; Ján Mináč; Lyle E Muller; Roberto C Budzinski

doi:10.1063/5.0161399

Composed solutions of synchronized patterns in multiplex networks of Kuramoto oscillators

Chaos. 2023 Oct 1;33(10):103128. doi: 10.1063/5.0161399.

Authors

Priya B Jain^{1

2

3}, Tung T Nguyen^{1

2

3}, Ján Mináč^{1

2

3}, Lyle E Muller^{1

2

3}, Roberto C Budzinski^{1

2

3}

Affiliations

¹ Department of Mathematics, Western University, London, Ontario N6A 3K7, Canada.
² Western Institute for Neuroscience, Western University, London, Ontario N6A 3K7, Canada.
³ Western Academy for Advanced Research, Western University, London, Ontario N6A 3K7, Canada.

PMID: 37844292
DOI: 10.1063/5.0161399

Abstract

Networks with different levels of interactions, including multilayer and multiplex networks, can display a rich diversity of dynamical behaviors and can be used to model and study a wide range of systems. Despite numerous efforts to investigate these networks, obtaining mathematical descriptions for the dynamics of multilayer and multiplex systems is still an open problem. Here, we combine ideas and concepts from linear algebra and graph theory with nonlinear dynamics to offer a novel approach to study multiplex networks of Kuramoto oscillators. Our approach allows us to study the dynamics of a large, multiplex network by decomposing it into two smaller systems: one representing the connection scheme within layers (intra-layer), and the other representing the connections between layers (inter-layer). Particularly, we use this approach to compose solutions for multiplex networks of Kuramoto oscillators. These solutions are given by a combination of solutions for the smaller systems given by the intra- and inter-layer systems, and in addition, our approach allows us to study the linear stability of these solutions.