Normal forms and centre manifold reductions for networks

• Grant number: 20/01100-2
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: November 01, 2021
• End date: October 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Tiago Pereira da Silva
• Grantee: Eeltje Cornelis Nijholt
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

A network encodes a structure of individual units (the nodes), together with the information of how these units depend on each other. We project focus on qualitative changes in the dynamics of networks as one or more parameters vary. One can, for example, think about the emergence of steady state points or periodic orbits, or the phenomenon where by multiple cells in a network start displaying identical dynamical behaviour (synchronisation). Due to the nature of network structures, the symmetries are often more "exotic" than compact groups; equivariance of a dynamical system will often mean with respect to the action of a finite monoid (i.e. a group without inverses) and there presentations in question will often be of semigroups. The project deals with such normal form reduction to understand how collective dynamics appear with such systems. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

NIJHOLT, EDDIE; PEREIRA, TIAGO; QUEIROZ, FERNANDO C.; TURAEV, DMITRY. Chaotic Behavior in Diffusively Coupled Systems. Communications in Mathematical Physics, v. 401, n. 3, p. 42-pg., 2023-04-03. (13/07375-0, 20/01100-2)