Synchrony in asymmetric coupled cell networks

• Grant number: 25/21600-3
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: February 06, 2026
• End date: June 05, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Míriam Garcia Manoel
• Grantee: Nícolas da Rocha Brito
• Supervisor: Ana Paula da Silva Dias
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Universidade do Porto (UP), Portugal
• Associated to the scholarship: 24/08713-0 - Networks of coupled dynamics in decision-making process, BP.MS

Abstract

This project focuses on the study of synchrony in networks of coupled dynamical systems in which the associated graph is undirected and asymmetric. The study of symmetries in graphs for the construction of invariant subspaces under the dynamics, called synchrony subspaces, is a subject addressed in several recent works. A subgroup of the automorphism group of the graph associated with the network induces a synchrony subspace, but the converse is not true, which gives rise to the concept of exotic synchrony. During the studies carried out so far, some results have already been established for the case of undirected tree graphs, characterizing that no exotic synchrony pattern exists for this class. For generically asymmetric networks, the presence of nontrivial synchronies is rare, and when they occur, they fall into patterns considered exotic. The present project aims to investigate what classes of undirected and asymmetric networks admit nontrivial synchrony. This investigation may be an important step towards better understanding the limit of the absence of graph symmetry for the occurrence of network synchrony. Such a study is directly relevant to decision-making processes, since the structure of the network of agents and options directly influences the attainment of consensus. (AU)