Work

Design of Stable Signed Laplacian Matrices with Mixed Attractive–Repulsive Couplings for Complete In-Phase Synchronization

Year: 2025

Type: article

Abstract: Synchronization in complex networks mainly considers positive (attractive) couplings to guarantee network stability. However, in many real-world systems or processes, negative (repulsive) interactions exist, and this poses a challenging problem. In this proposal, we present an algorithm to design stable signed Laplacian matrices with mixed attractive and repulsive couplings that ensure stability in both complete and in-phase synchronization. The main result is established through a constructive theorem that guarantees a single zero eigenvalue, while all other eigenvalues are negative, thereby preserving the diffusivity condition. The algorithm allows control over the spectral properties of the matrix by adjusting two parameters, which can be interpreted as a pole placement strategy from control theory. The approach is validated through numerical examples involving the synchronization of a network of chaotic Lorenz systems and a network of Kuramoto oscillators. In both cases, full synchronization is achieved despite the presence of negative couplings.

Source: Mathematics

DOI: 10.3390/math13172741

Authors: Gualberto Solis-Perales, Aurora Espinoza-Valdez, Beatriz C. Luna-Oliveros, Jorge Rivera, Jairo Sánchez-Estrada

Institutions: Universidad de Guadalajara, National Pedagogic University, Instituto Politécnico Nacional, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

OpenAlex ID: W4413698478

FWCI:

Cites: 41

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Related to: 10